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Symmetries Beget Symmetries: Ghostly Higher-Form Symmetries and the Descent Equation

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Pith's one-line read Currents with nonzero ghost number satisfying $dJ = QJ^{(1)}$ define topological higher-form symmetries, so every conventional higher-form symmetry begets a ladder of ghostly ones.

desk verdict A useful and mostly sound formal unpacking of descent-equation topological operators as 'ghostly' higher-form symmetries; the main physical claim needs work because the operators are shown to be Q-closed but not to act on physical states. read the letter →

arxiv 2509.15978 v2 pith:XLW7LYES submitted 2025-09-19 hep-th cond-mat.str-elmath-phmath.MP

Leron Borsten , Dimitri Kanakaris , Hyungrok Kim This is my paper · ORCID
classification hep-thcond-mat.str-elmath-phmath.MP
keywords higher-formsymmetriesghostnumberBatalin-VilkoviskyformalismdescentequationtopologicaloperatorsMaxwelltheoryYang-Millscentresymmetryhighergauge
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Through the Batalin–Vilkovisky formalism, the paper argues that a higher-form symmetry current need not be closed on the nose; it is enough that its exterior derivative is $Q$-exact, $dJ = QJ^{(1)}$. Iterating this descent equation yields currents of increasing form degree and decreasing ghost number, each of which generates a topological operator of the kind that defines a higher-form symmetry, so conventional symmetries beget 'ghostly' symmetries with nonzero ghost number. This matters because it turns the familiar descent equations of topological field theory and anomalies into machinery for generating new symmetries, and it gives those ghostly symmetries a physical role: they act on Wilson-type operators built from ghosts and antifields, and their surviving discrete subgroups match between ultraviolet and infrared. The authors verify the structure in Maxwell theory, Abelian higher gauge theory, Chern–Simons/BF theories, Yang-Mills centre symmetry, and adjusted higher gauge theory.

What carries the argument

The central object is the descent equation $dJ^{(i)}=QJ^{(i+1)}$ in the bigraded algebra of differential-form operators, where the two differentials are the de Rham differential $d$ (form degree plus one) and the BV differential $Q$ (ghost number plus one). It replaces the ordinary on-shell conservation law with a $Q$-exactness condition, so the operator $\exp(i\int_\Sigma J)$ is invariant under deformations of $\Sigma$ whenever $Q$ annihilates correlation functions. The paper organizes all rungs into the total complex with differential $D = d + (-1)^q Q$; solutions of $D\alpha=0$ are exactly the ghostly current families, and the space of solutions carries the forgetful maps that give the span of symmetry groups.

What would settle it

In free Maxwell theory on a four-torus, compute a correlation function of the ghostly zero-form symmetry operator $\exp(i\alpha\int_\Sigma A^+)$ with a physical $Q$-closed observable for two homologous cycles $\Sigma$; if the correlator changes under a smooth deformation of $\Sigma$, the ghostly current $A^+$ is not the generator of a genuine symmetry and the descent chain reduces to the known topological-operator statement.

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Extended reading notes

Core claim

The central claim is that a conserved higher-form current need only be closed up to the BV differential: if $dJ = QJ^{(1)}$, then $U(\Sigma)=\exp(i\int_\Sigma J)$ is a topological operator and defines a symmetry even when $J$ carries nonzero ghost number. Iterating the descent equations $dJ^{(i)}=QJ^{(i+1)}$ produces a chain of ghostly currents of increasing form degree and decreasing ghost number, and every non-terminal rung of the chain generates a higher-form symmetry. The paper packages the solutions into a span of group homomorphisms $G[p,q] \leftarrow G[p,q];[p+1,q-1] \rightarrow G[p+1,q-1]$, and verifies the structure in Maxwell theory, Abelian higher gauge theory, Chern–Simons/BF theories, Yang-Mills centre symmetries, and adjusted higher gauge theory.

Load-bearing premise

The argument treats operators built from ghost-number-carrying currents, $\exp(i\int_\Sigma J)$, as genuine symmetry operators whose correlation functions are annihilated by the BV differential $Q$, even though those operators act on ghosts and antifields in a non-positive-definite extended Fock space.

Editorial extensions

If this is right

  • In any theory where a conventional higher-form symmetry current satisfies $dJ = QJ^{(1)}$, the full descent chain produces additional topological operators of higher form degree and lower ghost number; these are the conserved charges of ghostly symmetries.
  • In topological theories the descent chain never terminates, so every rung is a symmetry current and the familiar topological observables of cohomological TQFTs can be reinterpreted as charges of ghostly higher-form symmetries.
  • In Maxwell and Abelian higher gauge theory, the electric symmetry begets ghostly zero-form and $(-1)$-form symmetries whose charges count ghost and antifield quanta in an extended Fock space, with corresponding Wilson-type operators transforming under the ghostly currents.
  • When charged matter is added, the continuous ghostly symmetries break to discrete subgroups, and these subgroups match between the ultraviolet theory and its infrared BF-like limit, giving a ghostly analogue of 't Hooft anomaly matching.
  • The Yang-Mills centre one-form symmetry begets ghostly zero-form and $(-1)$-form symmetries, and adjusted higher gauge theory has an even richer pattern descending from one-form, two-form, and ghostly one-form centre symmetries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Going beyond the paper: the span of symmetry groups suggests a spectral-sequence picture in which ghostly symmetries are higher-page cohomology of the double complex; if so, the symmetry ladders of a given theory could be computed algebraically without solving any dynamics.
  • Going beyond the paper: if the discrete subgroups of ghostly symmetries survive matter coupling, they could serve as new renormalization-group invariants, and a lattice simulation of topological operators built from ghosts could test whether the symmetry claim is realized in the continuum limit.
  • Going beyond the paper: the interpretation of ghostly charges as counting antifield excitations in a non-positive-definite Fock space suggests these symmetries act on unphysical states, so the physically robust content may be the topological constraints and anomaly-matching conditions they impose rather than any Hilbert-space charge.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper develops a Batalin–Vilkovisky (BV) perspective on higher-form symmetries. It observes that if a current J satisfies the descent equation dJ = Q J^(1), where Q is the BV differential, then the exponentiated operator U(Σ) = exp(iα∫_Σ J) is topological, independent of the ghost number of J. On this basis the paper introduces 'ghostly higher-form symmetries' G[p,q], i.e. higher-form symmetries whose currents carry nonzero ghost number q. It shows that standard (ghost-number-zero) higher-form symmetries generate such ghostly symmetries through chains of descent equations, and formalizes the structure as a span of group homomorphisms. The bulk of the paper consists of worked examples: free scalar theory, Maxwell theory, abelian higher gauge theory, Chern–Simons and BF theories, Yang–Mills centre symmetry, and adjusted higher gauge theory. It also discusses matter couplings, UV/IR matching, and a reinterpretation of Donaldson–Witten observables.

Significance. The intended contribution is a unification of the descent-equation technology of TQFTs and anomalies with the theory of generalized global symmetries, placing both in a common BV framework. The explicit computations in Sections 5–8 appear internally consistent, and the span construction (Section 3.2.2) provides a clean algebraic formulation. The paper is also commendable for treating discrete symmetries via Čech/cellular cochains and for constructing ghostly analogues in non-abelian settings. However, the physical status of the central claim is not settled. The operators constructed are Q-closed topological operators in the BV algebra, but it is not demonstrated that they act on the physical subspace H^0_Q or have a nontrivial action on physical observables. The Maxwell example (Section 5.1.2) explicitly locates the charges in an extended Fock space with a non-positive-definite inner product, acting on ghosts and antifields. If the ghostly operators do not act on physical states, the claim reduces to the known statement that descent equations produce topological operators. This gap is load-bearing for the paper's central assertion that ghostly currents define symmetries.

major comments (4)
  1. [Section 3.1, Eqs. (25)–(27)] The proof that U(Σ)=exp(iα∫_Σ J) is topological uses only the descent equation dJ=QJ^(1) and the assumption that Q annihilates correlation functions. This establishes that U(Σ) is a Q-closed operator in the BV algebra, but it does not establish that U(Σ) preserves the physical subspace H^0_Q or acts nontrivially on physical observables. The Maxwell example in Section 5.1 illustrates the gap: the zero-form current A^+ and the (d-1)-form current c act on ghost/antifield variables, and no physical observable is shown to transform under them. To sustain the claim that ghostly currents define symmetries of the physical theory, the authors should prove, or at least demonstrate in the examples, that the charges are not Q-exact on H^0_Q and that they have a nontrivial action on Q-closed observables. Otherwise the statement reduces to the known fact that descent equations produce topological operators in the BV algebra.
  2. [Section 5.1.2] The interpretation in terms of an extended Fock space with a non-positive-definite inner product makes explicit that ghostly charges count excitations of ghosts and antifields. This supports the view that the symmetries act on the BV-extended field space rather than on physical states. The paper should clarify whether 'ghostly symmetry' is intended as a symmetry of the BV-extended theory only (in which case the terminology should be adjusted to avoid implying a symmetry of the quantum theory) or as a symmetry of the physical quantum theory (in which case the missing demonstration of nontrivial action on H^0_Q is essential).
  3. [Section 3.1, first paragraph] A p-form symmetry is defined as a topological invertible operator inserted on a codimension-(p+1) submanifold. Under this definition, the statement that any solution of the descent equation dJ=QJ^(1) defines a higher-form symmetry is near-tautological, because the descent equation is exactly what makes the exponentiated operator topological. The paper should explain what additional content is being claimed beyond the existing descent-equation formalism for topological operators (e.g., refs. [43,50-52]), and should provide a criterion that distinguishes a nontrivial ghostly symmetry from a Q-exact or d-exact current. The current cohomology (41) partially addresses the latter, but its physical interpretation remains unclear.
  4. [Sections 5.4.1 and 7.3] The UV/IR matching of ghostly symmetries is performed at the level of identifying currents and their descent equations. Since the charges have not been shown to act on physical states, the matching of these ghostly symmetries does not yet provide a physical constraint analogous to 't Hooft anomaly matching. A demonstration that the matched charges are nonvanishing and act on local operators in the physical Hilbert spaces of both the UV and IR theories would be needed to give the matching physical teeth.
minor comments (5)
  1. [Introduction, p. 3] There is a typo: 'decent equations' should be 'descent equations' in the sentence 'More recently, the decent equations have appeared in constructions of symmetry topological field theories.'
  2. [Section 7.3, p. 46] In the last sentence, 'as given in (13)' should presumably refer to Fig. 13, not an equation number.
  3. [Section 3.2.2, Eqs. (41)–(44)] The notation im 𝒜(𝑄) and im 𝒜(d) is used before being defined. The authors should explicitly state that these are the images of the operators acting on the algebra of local operators 𝒜.
  4. [Section 6] The assertion that Donaldson–Witten observables 𝒪^(i) constitute Noether currents for ghostly symmetries requires a coupling of the form (131) to some external sector; without such a coupling, the operators do not act on anything within the theory. The paper should state this more explicitly.
  5. [Figures 4, 13, 14] The figures are rich and useful, but the crossed-out entries (e.g., the crossed-out A in Fig. 4) are only explained in the caption of Fig. 4; the same convention should be stated in the captions of Figs. 13 and 14.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the descent-equation construction is self-contained, and same-author citations are background rather than load-bearing.

full rationale

The central kinematic step is eq. (27): given dJ = QJ^(1) and Q-annihilation of correlation functions, the operator U(Sigma) = exp(i alpha int_Sigma J) is deformation-invariant. This is a proof, not an assumption, and the subsequent identification of the J^(i) as ghostly higher-form symmetries is an application of the paper's explicit definition of a p-form symmetry as a topological invertible operator. The concrete content lies in the BV computations, such as the Maxwell descent towers (79)-(82), the Yang-Mills centre chain (146)-(147), and the higher-gauge diagram in fig. 14, none of which is presupposed by the general descent argument. The citations to the authors' own prior work ([40], [54], [97]) supply background definitions and previously established non-ghostly centre-symmetry groups; the new ghostly descendants are derived in the present paper rather than imported. Section 6 is explicitly a reinterpretation of Witten-type TQFT observables, not a new derivation. The paper also openly states in Sec. 5.1.2 that the ghostly charges act in an extended Fock space with non-positive-definite inner product and non-unitary BV dynamics, an acknowledged interpretational limitation rather than a hidden circular reduction. The only mild definitional closeness is that structural statements such as the span (1) are nearly restatements of the descent-equation solution space, but they are presented as organizational formalism rather than as empirical predictions. No fitted parameter is renamed as a prediction, and no uniqueness claim is imported from self-citations.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

The paper's central claim rests on the BV formalism and on a definitional extension of 'symmetry' to include topological operators of nonzero ghost number. No free parameters are fitted. The main novel postulate is the existence and physical status of ghostly symmetries, which act on BV-extended Fock space (ghosts/antifields) rather than on physical states.

assumptions (4)
  • domain assumption The BV operator Q commutes with the de Rham differential d and annihilates correlation functions of observables.
    Used to show that dJ = QJ^(1) makes U(Sigma) topological (Section 3.1, eq. (27)). This is standard BV but is an assumption about the quantum theory.
  • standard math The double complex of local differential-form operators A^{p,q} with differentials d and Q is a valid model for the space of observables.
    Section 2.1.1 defines A^{p,q}; the entire cohomological formulation depends on this structure.
  • ad hoc to paper Local operators of nonzero ghost number are legitimate symmetry generators whose exponentials are well-defined operators.
    Postulated in Section 1 ('Thus we are led to postulate the existence of ghostly p-form symmetries G[p,q]') and used throughout; no independent physical derivation is given.
  • standard math Discrete symmetries can be treated by replacing differential forms with cellular/Čech cocycles with coefficients in an Abelian group.
    Used for discrete centre symmetries in Section 7 following [54].
invented entities (1)
  • Ghostly higher-form symmetries G[p,q]
    purpose: Extend generalized global symmetries to currents with nonzero ghost number; unify descent-equation topological operators as symmetries.
    Introduced as a postulate in Section 1. No independent falsifiable handle is provided outside the BV formalism.

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Pith. "Pith review of Symmetries Beget Symmetries: Ghostly Higher-Form Symmetries and the Descent Equation." pith.science (2026). https://pith.science/paper/XLW7LYES

@misc{pith2026250915978,
  author       = {Pith},
  title        = {Pith review of: Symmetries Beget Symmetries: Ghostly Higher-Form Symmetries and the Descent Equation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XLW7LYES}},
  note         = {Machine review of arXiv:2509.15978}
}
read the original abstract

Viewed through the lens of the Batalin-Vilkovisky formalism, we demonstrate that higher-form currents with nonzero ghost number also define higher-form symmetries, directly analogous to the standard higher-form symmetries with ghost number zero. These ghostly higher symmetries descend from and into conventional higher-form symmetries via chains of descent equations familiar from the theory of anomalies and topological field theories. We give examples of such chains of ghostly symmetries in Maxwell theory, Abelian and non-Abelian higher gauge theory, Yang-Mills theory, and beyond.

Figures

Figures reproduced from arXiv: 2509.15978 by the authors.

Figure 1
Figure 1. In a descent chain, the endpoints 𝛼 (𝑚) and 𝛼 (𝑛) are not symmetries if the chain cannot continue, but the middle terms 𝛼 (𝑚+1) , . . . , 𝛼 (𝑛−1) are always symmetries. 𝑄-closed up to d-exact terms (i.e. is physical), then it must be d-closed up to 𝑄-exact terms (i.e. must be topological). Thus, the descent chain always extends indefinitely in downward (eventually hitting zero due to form degree reasons); indeed, th… view at source ↗
Figure 2
Figure 2. Ghostly higher-form symmetries of a free scalar field theory. The [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. The double complex 𝒜𝑝,𝑞 for Maxwell theory, where we only indicate those spaces containing 𝑝-form operators. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Ghostly higher-form symmetries of pure Maxwell theory in [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]
Figure 5
Figure 5. Figure 5: Ghostly higher symmetries of 𝑝-form Abelian gauge theory 28 [PITH_FULL_IMAGE:figures/full_fig_p028_5.png]
Figure 6
Figure 6. Figure 6: Ghostly symmetries of three-dimensional Abelian Chern–Simons [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]
Figure 7
Figure 7. Figure 7: Ghostly symmetries of 𝐵𝐹 theory with level 𝑞 and D𝛼 CS = 0 imposes precisely (104). There are no D-exact total degree 1 forms (as there are no total degree 0 forms) so the only non-empty cohomology is H1 D (Tot• (𝒜))  Ê 𝑝,𝑞 𝒜𝑝,𝑞 (106) The (ghostly) higher-form symmetr…
Figure 8
Figure 8. Figure 8: Ghostly higher-form symmetries of Maxwell theory in [PITH_FULL_IMAGE:figures/full_fig_p034_8.png]
Figure 9
Figure 9. Figure 9: Ghostly higher-form symmetries of the infrared limit of Maxwell [PITH_FULL_IMAGE:figures/full_fig_p035_9.png]
Figure 10
Figure 10. Figure 10: Ghostly higher symmetries of 𝑝-form Abelian gauge theory with sources of charge 𝑞 coupled to the one-form ghost 𝛬𝑝−1 (only lower form degrees shown) 37 [PITH_FULL_IMAGE:figures/full_fig_p037_10.png]
Figure 11
Figure 11. Figure 11: Ghostly symmetries corresponding to a descent chain of topological [PITH_FULL_IMAGE:figures/full_fig_p039_11.png]
Figure 12
Figure 12. Figure 12: Ghostly higher-form symmetries of 𝑑-dimensional 𝐺˜-valued Yang– Mills theory, where 𝐺˜ is a centreless compact Lie group current d𝑔, which is a Z(𝐺)-valued two-form19. Of course, this is entirely equivalent to the usual statement that the magnetic symmetry is π1(𝐺˜)-v…
Figure 13
Figure 13. Figure 13: Ghostly higher-form symmetries of 𝑑-dimensional 𝐺-valued Yang– Mills theory, where 𝐺 is a simply connected compact Lie group. Note that this figure and fig. 12 combined mimic the symmetries of Maxwell theory given in fig. 4. exact in the sense that it is the different…
Figure 14
Figure 14. Figure 14: Ghostly higher-form symmetries of adjusted higher gauge theory [PITH_FULL_IMAGE:figures/full_fig_p050_14.png]

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Reference graph

Works this paper leans on

111 extracted references · 16 canonical work pages · cited by 2 Pith papers

  1. [1]

    Generalized globalsymmetries.JournalofHighEnergyPhysics,2015(02):172,February 2015.arXiv:1412.5148,doi:10.1007/JHEP02(2015)172

    Davide Silvano Achille Gaiotto, Anton Nikolaevich Kapustin (Антон Николаевич Капустин),NathanSeiberg,andBrianWillett. Generalized globalsymmetries.JournalofHighEnergyPhysics,2015(02):172,February 2015.arXiv:1412.5148,doi:10.1007/JHEP02(2015)172

    arXiv 2015

  2. [2]

    Dumitrescu, Kenneth A

    Clay Córdova, Thomas T. Dumitrescu, Kenneth A. Intriligator, and Shu- Heng Shao (邵書珩). Snowmass white paper: Generalized symmetries in quantum field theory and beyond, May 2022.arXiv:2205.09545, doi:10.48550/arXiv.2205.09545

    arXiv doi:10.48550/arxiv.2205.09545 2022

  3. [3]

    Introduction to generalized global symmetries in QFT and particle physics, June 2023

    Theodore Daniel Brennan and Sungwoo Hong (홍성ᄋ ᅮ). Introduction to generalized global symmetries in QFT and particle physics, June 2023. arXiv:2306.00912,doi:10.48550/arXiv.2306.00912

    arXiv doi:10.48550/arxiv.2306.00912 2023

  4. [4]

    Anintroductiontohigher-formsymmetries

    PedroRogérioSérgiGomes. Anintroductiontohigher-formsymmetries. SciPost Physics Lecture Notes, 74:1–56, September 2023.arXiv:2303. 01817,doi:10.21468/SciPostPhysLectNotes.74

    doi:10.21468/scipostphyslectnotes.74 2023

  5. [5]

    Bottini, Ludovic Fraser-Taliente, Liam Glad- den, Dewi Sid William Gould, Arthur Platschorre, and Hannah Tillim

    Lakshya Bhardwaj, Lea E. Bottini, Ludovic Fraser-Taliente, Liam Glad- den, Dewi Sid William Gould, Arthur Platschorre, and Hannah Tillim. Lecturesongeneralizedsymmetries.PhysicsReports,1051:1–87,February 2024.arXiv:2307.07547,doi:10.1016/j.physrep.2023.11.002

    arXiv 2024

  6. [6]

    Lecture notes on generalized symmetries and applications.Physics Reports, 1065:1–43, May 2024

    Ran Luo (罗然), Qing-Rui Wang (王晴睿), and Yi-Nan Wang (王一男). Lecture notes on generalized symmetries and applications.Physics Reports, 1065:1–43, May 2024. arXiv:2307.09215, doi:10.1016/j. physrep.2024.02.002

    arXiv 2024

  7. [7]

    Quark confinement and topology of gauge groups.Nuclear Physics B, 120(3):429–458, March 1977.doi:10.1016/0550-3213(77)90086-4

    Alexander Markovich Polyakov ( Александр Маркович Поляков) . Quark confinement and topology of gauge groups.Nuclear Physics B, 120(3):429–458, March 1977.doi:10.1016/0550-3213(77)90086-4

    doi:10.1016/0550-3213(77)90086-4 1977

  8. [8]

    Com- pactgaugefieldsandtheinfraredcatastrophe.PhysicsLettersB,59(1):82– 84, October 1975.doi:10.1016/0370-2693(75)90162-8

    AlexanderMarkovichPolyakov( Александр Маркович Поляков). Com- pactgaugefieldsandtheinfraredcatastrophe.PhysicsLettersB,59(1):82– 84, October 1975.doi:10.1016/0370-2693(75)90162-8

    doi:10.1016/0370-2693(75)90162-8 1975

Show all 111 references
  1. [9]

    On the phase transition towards permanent quark confinement.Nuclear Physics B, 138(1):1–25, June 1978.doi:10.1016/ 0550-3213(78)90153-0

    Gerardus ’t Hooft. On the phase transition towards permanent quark confinement.Nuclear Physics B, 138(1):1–25, June 1978.doi:10.1016/ 0550-3213(78)90153-0

    1978

  2. [10]

    Alexander Kovner and Baruch Rosenstein. New look at QED4: The photon as a Goldstone boson and the topological interpretation of electric charge.Physical Review D, 49(10):5571–5581, May 1994.arXiv: hep-th/9210154,doi:10.1103/PhysRevD.49.5571

    1994 arXiv

  3. [11]

    Discrete gauge theories

    Mark Dirk Frederik de Wild Propitius and Ferdinand Alexander Bais. Discrete gauge theories. In Gordon Walter Semenoff and 52 Luc Vinet, editors,Particles and Fields, CRM Series in Mathematical Physics, pages 353–439, New York City, New York, United States of America, December ...

    1998 arXiv

  4. [12]

    Neworderparamet- ers for non-abelian gauge theories.Nuclear Physics B, 369(1–2):276–298, January 1992.doi:10.1016/0550-3213(92)90387-Q

    MarkGowerAlfordandJohnDavidMarch-Russell. Neworderparamet- ers for non-abelian gauge theories.Nuclear Physics B, 369(1–2):276–298, January 1992.doi:10.1016/0550-3213(92)90387-Q

    1992 doi

  5. [13]

    On detecting discrete Cheshire charge.Nuclear Phys- ics B, 386(1):27–42, November 1992

    Martin Aaron Bucher, Kai-Ming Lee ( 李啟明 ), and John Phillip Preskill. On detecting discrete Cheshire charge.Nuclear Phys- ics B, 386(1):27–42, November 1992. arXiv:hep-th/9112040, doi: 10.1016/0550-3213(92)90174-A

    1992 arXiv

  6. [14]

    Pantev and Eric Redmund Sharpe

    Tony G. Pantev and Eric Redmund Sharpe. Notes on gauging noneffective group actions, February 2005. arXiv:hep-th/0502027, doi:10.48550/arXiv.hep-th/0502027

    2005 doi arXiv

  7. [15]

    PantevandEricRedmundSharpe

    TonyG. PantevandEricRedmundSharpe. GLSMsforgerbes(andother toricstacks).AdvancesinTheoreticalandMathematicalPhysics,10(1):77–121, 2006.arXiv:hep-th/0502053,doi:10.4310/ATMP.2006.v10.n1.a4

    2006 arXiv

  8. [16]

    Pantev,EricRedmund Sharpe,andMatthewAndo

    SimeonHellerman,AndréGilHenriques,TonyG. Pantev,EricRedmund Sharpe,andMatthewAndo. Clusterdecomposition,T-duality,andgerby CFTs.Advances in Theoretical and Mathematical Physics, 11(5):751–818, 2007.arXiv:hep-th/0606034,doi:10.4310/ATMP.2007.v11.n5.a2

    2007 arXiv

  9. [17]

    Asymmetryprinciplefortopological quantum order.Annals of Physics, 324(5):977–1057, May 2009.arXiv: cond-mat/0702377,doi:10.1016/j.aop.2008.11.002

    ZoharNussinovandGerardoOrtíz. Asymmetryprinciplefortopological quantum order.Annals of Physics, 324(5):977–1057, May 2009.arXiv: cond-mat/0702377,doi:10.1016/j.aop.2008.11.002

    2009 arXiv

  10. [18]

    Higher symmetry and gapped phases of gauge theories

    AntonNikolaevichKapustin( Антон Николаевич Капустин)andRyan Thorngren. Higher symmetry and gapped phases of gauge theories. In DenisAuroux,LudmilVasilevKatzarkov( Людмил Василев Кацарков), Tony G. Pantev, Yan Sergeevich Soibelman (Яков Сергеевич Сойбель- ман), and Yuri Tschink...

    2017 arXiv

  11. [19]

    Re- lativistic 𝑆-matrix of dynamical systems with boson and fermion constraints.Physics Letters B, 69(3):309–312, August 1977

    IgorAnatolievichBatalin( Игорь Анатольевич Баталин)andGrigoryAl- exandrovichVilkovisky( Григорий Александрович Вилковыский). Re- lativistic 𝑆-matrix of dynamical systems with boson and fermion constraints.Physics Letters B, 69(3):309–312, August 1977. doi: 10.1016/0370-2693(77)90553-6

    1977 doi

  12. [20]

    53 Gauge algebra and quantization.Physics Letters B, 102(1):27–31, June 1981.doi:10.1016/0370-2693(81)90205-7

    IgorAnatolievichBatalin( Игорь Анатольевич Баталин)andGrigoryAl- exandrovich Vilkovisky (Григорий Александрович Вилковыский) . 53 Gauge algebra and quantization.Physics Letters B, 102(1):27–31, June 1981.doi:10.1016/0370-2693(81)90205-7

    1981 doi

  13. [21]

    Quantization of gauge theories with linearly dependent generators

    IgorAnatolievichBatalin( Игорь Анатольевич Баталин)andGrigoryAl- exandrovich Vilkovisky (Григорий Александрович Вилковыский) . Quantization of gauge theories with linearly dependent generators. Physical Review D, 28(10):2567–2582, November 1983.doi:10.1103/ PhysRevD.28.2567

    1983

  14. [22]

    Closure of the gauge algebra, generalized Lie equations and Feyn- man rules.Nuclear Physics B, 234(1):106–124, March 1984

    IgorAnatolievichBatalin( Игорь Анатольевич Баталин)andGrigoryAl- exandrovich Vilkovisky (Григорий Александрович Вилковыский) . Closure of the gauge algebra, generalized Lie equations and Feyn- man rules.Nuclear Physics B, 234(1):106–124, March 1984. doi: 10.1016/0550-3213(84)90227-X

    1984 doi

  15. [23]

    Ex- istence theorem for gauge algebra.Journal of Mathematical Physics, 26(1):172–184, January 1985.doi:10.1063/1.526780

    IgorAnatolievichBatalin( Игорь Анатольевич Баталин)andGrigoryAl- exandrovichVilkovisky( Григорий Александрович Вилковыский). Ex- istence theorem for gauge algebra.Journal of Mathematical Physics, 26(1):172–184, January 1985.doi:10.1063/1.526780

    1985 doi

  16. [24]

    Lectures on the antifield-BRST formalism for gauge theories.Nuclear Physics B – Proceedings Supplement, 18(1):47–106, December 1990.doi:10.1016/0920-5632(90)90647-D

    Marc Henneaux. Lectures on the antifield-BRST formalism for gauge theories.Nuclear Physics B – Proceedings Supplement, 18(1):47–106, December 1990.doi:10.1016/0920-5632(90)90647-D

    1990 doi

  17. [25]

    PrincetonUniversityPress,Princeton,NewJersey,United States of America, 1992.doi:10.2307/j.ctv10crg0r

    Marc Henneaux and Claudio Teitelboim Weitzman.Quantization of GaugeSystems. PrincetonUniversityPress,Princeton,NewJersey,United States of America, 1992.doi:10.2307/j.ctv10crg0r

    1992 doi

  18. [26]

    Antibracket, antifieldsandgaugetheoryquantization.PhysicsReports,259(1–2):1–145, August 1995

    Joaquím Gomis Torné, Jordi París, and Stuart Samuel. Antibracket, antifieldsandgaugetheoryquantization.PhysicsReports,259(1–2):1–145, August 1995. arXiv:hep-th/9412228, doi:10.1016/0370-1573(94) 00112-G

    1995 arXiv

  19. [27]

    Local BRST cohomology in gauge theories.Physics Reports, 338(5):439–569, Novem- ber 2000

    Glenn Barnich, Friedemann Brandt, and Marc Henneaux. Local BRST cohomology in gauge theories.Physics Reports, 338(5):439–569, Novem- ber 2000. arXiv:hep-th/0002245, doi:10.1016/S0370-1573(00) 00049-1

    arXiv

  20. [28]

    An introduction to the Batalin-Vilkovisky formal- ism,February2004

    Domenico Fiorenza. An introduction to the Batalin-Vilkovisky formal- ism,February2004. arXiv:math/0402057, doi:10.48550/arXiv.math/ 0402057

    doi arXiv

  21. [29]

    BRST quantization: A short review.International Journal of Geometric Meth- ods in Modern Physics, 2:939–964, 2005

    Andrea Fuster, Marc Henneaux, and Axel Torsten Maas. BRST quantization: A short review.International Journal of Geometric Meth- ods in Modern Physics, 2:939–964, 2005. arXiv:hep-th/0506098, doi:10.1142/S0219887805000892. 54

    2005 arXiv

  22. [30]

    Introduction to graded geometry, Batalin-Vilkovisky formalism and their applica- tions.Archivum Mathematicum, 47(5):143–199, 2011.arXiv:1105.2680, doi:10338.dmlcz/141789

    Jian Qiu and Maxim Zabzine (Максим Забзин). Introduction to graded geometry, Batalin-Vilkovisky formalism and their applica- tions.Archivum Mathematicum, 47(5):143–199, 2011.arXiv:1105.2680, doi:10338.dmlcz/141789

    2011 arXiv

  23. [31]

    Lectures on Batalin-Vilkoviskyformalismanditsapplicationsintopologicalquantum field theory, July 2017.arXiv:1707.08096, doi:10.48550/arXiv.1707

    Pavel Nikolaevich Mnev (Павел Николаевич Мнёв) . Lectures on Batalin-Vilkoviskyformalismanditsapplicationsintopologicalquantum field theory, July 2017.arXiv:1707.08096, doi:10.48550/arXiv.1707. 08096

    2017 doi arXiv

  24. [32]

    Introduction to classical gauge field theory and to Batalin-Vilkovisky quantization, September 2018

    Glenn Barnich and Fabrizio Del Monte. Introduction to classical gauge field theory and to Batalin-Vilkovisky quantization, September 2018. arXiv:1810.00442,doi:10.48550/arXiv.1810.00442

    2018 doi arXiv

  25. [33]

    Introduction to the BV-BFV formalism.Reviews in Mathematical Physics, 32(09):2030006, October 2020.arXiv:1905.08047,doi:10.1142/S0129055X2030006X

    Alberto Sergio Cattaneo and Nima Moshayedi. Introduction to the BV-BFV formalism.Reviews in Mathematical Physics, 32(09):2030006, October 2020.arXiv:1905.08047,doi:10.1142/S0129055X2030006X

    2020 arXiv

  26. [34]

    American Mathematical Society, Providence, RhodeIsland, UnitedStatesofAmerica, 2019

    Pavel Nikolaevich Mnev (Павел Николаевич Мнёв).Quantum Field Theory: Batalin–Vilkovisky Formalism and its Applications, volume 72 of University Lecture Series. American Mathematical Society, Providence, RhodeIsland, UnitedStatesofAmerica, 2019. doi:10.1090/ulect/072

    2019 doi

  27. [35]

    BV quantization

    Alberto Sergio Cattaneo, Pavel Nikolaevich Mnev (Павел Николаевич Мнёв), and Michele Schiavina. BV quantization. In Richard Joseph Szabo and Martin Bojowald, editors,Encyclopedia of Mathematical Physics, volume 5, pages 543–555. Academic Press, Cambridge, Massachusetts, United...

    2025 arXiv

  28. [36]

    Extended antifield formalism.Nuclear Physics B, 510(3):640–656, January 1998

    Friedemann Brandt, Marc Henneaux, and André Wilch. Extended antifield formalism.Nuclear Physics B, 510(3):640–656, January 1998. arXiv:hep-th/9705007,doi:10.1016/S0550-3213(97)00681-0

    1998 arXiv

  29. [37]

    Ward identities for rigid symmetries of higher order, November 1996.arXiv:hep-th/ 9611056,doi:10.48550/arXiv.hep-th/9611056

    Friedemann Brandt, Marc Henneaux, and André Wilch. Ward identities for rigid symmetries of higher order, November 1996.arXiv:hep-th/ 9611056,doi:10.48550/arXiv.hep-th/9611056

    1996 doi arXiv

  30. [38]

    Globalsymmet- ries in the antifield formalism.Physics Letters B, 387(2):320–326, October 1996.arXiv:hep-th/9606172,doi:10.1016/0370-2693(96)01034-9

    FriedemannBrandt,MarcHenneaux,andAndréWilch. Globalsymmet- ries in the antifield formalism.Physics Letters B, 387(2):320–326, October 1996.arXiv:hep-th/9606172,doi:10.1016/0370-2693(96)01034-9

    1996 arXiv

  31. [39]

    Background fields in the presymplectic BV-AKSZ approach, May 2025

    Ivan Dmitrievich Dneprov ( Иван Дмитриевич Днепров) and Maxim Anatolievich Grigoriev ( Григорьев Максим Анатольевич) . Background fields in the presymplectic BV-AKSZ approach, May 2025. arXiv:2505.09885,doi:10.48550/arXiv.2505.09885

    2025 doi

  32. [40]

    SandwichconstructionofsymmetryTFTsforthecentresymmetries 55 of Chern-Simons, Yang-Mills, and Einstein gravity, September 2025

    Leron Borsten, Dimitri Kanakaris Decavel, and Hyungrok Kim (金炯 錄). SandwichconstructionofsymmetryTFTsforthecentresymmetries 55 of Chern-Simons, Yang-Mills, and Einstein gravity, September 2025. arXiv:2509.08819,doi:10.48550/arXiv.2509.08819

    2025 doi arXiv

  33. [41]

    Topological quantum field theory.Communications in Mathematical Physics, 117(3):353, September 1988

    Edward Witten. Topological quantum field theory.Communications in Mathematical Physics, 117(3):353, September 1988. doi:10.1007/ BF01223371

    1988

  34. [42]

    Lectures on topological quantum field theory.AIP Con- ference Proceedings, 419(1):54–93, January 1998.arXiv:hep-th/9709192, doi:10.1063/1.54705

    José Manuel Fernández de Labastida y del Olmo and Carlos Loz- ano Rodríguez. Lectures on topological quantum field theory.AIP Con- ference Proceedings, 419(1):54–93, January 1998.arXiv:hep-th/9709192, doi:10.1063/1.54705

    1998 arXiv

  35. [43]

    Springer, Dordrecht, the Netherlands, 2005.doi:10.1007/1-4020-3177-7

    José Manuel Fernández de Labastida y del Olmo and Marcos Mar- iñoBeiras.TopologicalQuantumFieldTheoryandFourManifolds. Springer, Dordrecht, the Netherlands, 2005.doi:10.1007/1-4020-3177-7

    2005 doi

  36. [44]

    Quantum field theory and differential geometry

    Wen-feng Chen. Quantum field theory and differential geometry. International Journal of Geometric Methods in Modern Physics, 10:1350003, 2013.arXiv:0803.1340,doi:10.1142/S0219887813500035

    2013 arXiv

  37. [45]

    Continuum gauge theories

    Raymond Félix Stora. Continuum gauge theories. In Maurice Lévy and Pronob K. Mitter, editors,New Developments in Quantum Field Theory and Statistical Mechanics: Cargèse 1976, volume 26 ofNato Advanced Study InstitutesSeriesB,pages201–224,NewYorkCity,NewYork,UnitedStates of Ame...

    1976 doi

  38. [46]

    Algebraic structure and topological origin of anomalies

    Raymond Félix Stora. Algebraic structure and topological origin of anomalies. In Gerardus ’t Hooft, Arthur Michael Jaffe, Harry Lehmann, Pronob K. Mitter, Isadore Manuel Singer, and Raymond Félix Stora, editors,ProgressinGaugeFieldTheory,volume115ofNatoAdvancedStudy Institutes...

    1984 doi

  39. [47]

    Course 12

    Bruno Zumino. Course 12. Chiral anomalies and differential geometry. In Bryce Seligmann DeWitt and Raymond Félix Stora, editors,Relativité, Groupes et Topologie II. Les Houches 1983, Session XL, pages 1291–1322, Amsterdam, the Netherlands, 1984. North-Holland

    1983

  40. [48]

    Chiral anomalies, higher dimensions, and differential geometry.Nuclear Physics B, 239(2):477–507, July 1984

    Bruno Zumino, Yong-Shi Wu (吴咏时), and Anthony Zee (徐一鴻). Chiral anomalies, higher dimensions, and differential geometry.Nuclear Physics B, 239(2):477–507, July 1984. doi:10.1016/0550-3213(84) 90259-1

    1984 doi

  41. [49]

    Cohomology of gauge groups: Cocycles and Schwinger terms.Nuclear Physics B, 253:477–493, 1985

    Bruno Zumino. Cohomology of gauge groups: Cocycles and Schwinger terms.Nuclear Physics B, 253:477–493, 1985. doi: 10.1016/0550-3213(85)90543-7. 56

    1985 doi

  42. [50]

    Clar- endon Press, Oxford, United Kingdom, 1996.doi:10.1093/acprof: oso/9780198507628.001.0001

    Reinhold Anton Bertlmann.Anomalies in Quantum Field Theory. Clar- endon Press, Oxford, United Kingdom, 1996.doi:10.1093/acprof: oso/9780198507628.001.0001

    1996

  43. [51]

    TASI 2003 lectures on anomalies, September 2005

    Jeffrey Alan Harvey. TASI 2003 lectures on anomalies, September 2005. arXiv:hep-th/0509097,doi:10.48550/arXiv.hep-th/0509097

    2003 doi arXiv

  44. [52]

    Lectures on anomalies, February 2008.arXiv:0802.0634, doi:10.48550/arXiv.0802.0634

    Adel Bilal. Lectures on anomalies, February 2008.arXiv:0802.0634, doi:10.48550/arXiv.0802.0634

    2008 doi arXiv

  45. [53]

    SymTFTsfor U(1)symmetries from descent, November 2024

    FinnGaglianoandIñakiGarcíaEtxebarria. SymTFTsfor U(1)symmetries from descent, November 2024. arXiv:2411.15126, doi:10.48550/ arXiv.2411.15126

    2024 doi arXiv

  46. [54]

    Discrete𝑝-form symmetry and higher Coulomb phases, July 2025.arXiv:2507.10459, doi:10

    Leron Borsten and Hyungrok Kim (金炯錄). Discrete𝑝-form symmetry and higher Coulomb phases, July 2025.arXiv:2507.10459, doi:10. 48550/arXiv.2507.10459

    2025 doi arXiv

  47. [55]

    𝐿∞-algebras of classical field theories and the Batalin–Vilkovisky formalism.Fortschritte der Physik, 67(7):1900025, July 2019

    Branislav Jurčo, Lorenzo Raspollini, Christian Sämann, and Martin Wolf. 𝐿∞-algebras of classical field theories and the Batalin–Vilkovisky formalism.Fortschritte der Physik, 67(7):1900025, July 2019. arXiv: 1809.09899,doi:10.1002/prop.201900025

    2019 arXiv

  48. [56]

    Cambridge University Press, Cambridge, United Kingdom, September 2021.doi:10.1017/9781316678664

    Kevin Joseph Costello and Owen Gwilliam.Factorization Algebras in Quantum Field Theory: Volume II, volume 41 ofNew Mathematical Monographs. Cambridge University Press, Cambridge, United Kingdom, September 2021.doi:10.1017/9781316678664

    2021 doi

  49. [57]

    Cambridge University Press, Cambridge, United Kingdom, December 2016.doi:10.1017/9781316678626

    Kevin Joseph Costello and Owen Gwilliam.Factorization Algebras in Quantum Field Theory: Volume I, volume 31 ofNew Mathematical Monographs. Cambridge University Press, Cambridge, United Kingdom, December 2016.doi:10.1017/9781316678626

    2016 doi

  50. [58]

    Classical and quantum Lagrangian field theories with bound- ary.Proceedings of Science, 155:044, August 2011

    Alberto Sergio Cattaneo, Pavel Nikolaevich Mnev (Павел Николаевич Мнёв), and Nicolai Yurievich Reshetikhin (Николай Юрьевич Реше- тихин). Classical and quantum Lagrangian field theories with bound- ary.Proceedings of Science, 155:044, August 2011. arXiv:1207.0239, doi:10.22323...

    2011 arXiv

  51. [59]

    Classical BV theories on manifolds with boundary.Commu- nications in Mathematical Physics, 332:535–603, 2014.arXiv:1201.0290, doi:10.1007/s00220-014-2145-3

    Alberto Sergio Cattaneo, Pavel Nikolaevich Mnev (Павел Николаевич Мнёв), and Nicolai Yurievich Reshetikhin (Николай Юрьевич Реше- тихин). Classical BV theories on manifolds with boundary.Commu- nications in Mathematical Physics, 332:535–603, 2014.arXiv:1201.0290, doi:10.1007/s...

    2014 arXiv

  52. [60]

    Perturbative quantum gauge theories on manifolds with boundary.Communications in Mathematical Physics, 357(2):631–730, 2018

    Alberto Sergio Cattaneo, Pavel Nikolaevich Mnev (Павел Николаевич Мнёв), and Nicolai Yurievich Reshetikhin (Николай Юрьевич Реше- тихин). Perturbative quantum gauge theories on manifolds with boundary.Communications in Mathematical Physics, 357(2):631–730, 2018. arXiv:1507.012...

    2018 arXiv

  53. [61]

    Notes on supersym- metry (following Joseph Bernstein)

    Pierre René Deligne and John Willard Morgan. Notes on supersym- metry (following Joseph Bernstein). In Pierre René Deligne, Pavel Ilyich Etingof (Павел Ильич Этингоф), Daniel Stuart Freed, Lisa Claire Jef- frey, David Kazhdan, John Willard Morgan, David Robert Morrison, and Ed...

    1999

  54. [62]

    Cambridge University Press, Cambridge, United Kingdom, December 2001

    Allen Edward Hatcher.Algebraic Topology. Cambridge University Press, Cambridge, United Kingdom, December 2001. URL: https: //pi.math.cornell.edu/~hatcher/AT/ATpage.html

    2001

  55. [63]

    Springer Monographs in Mathematics

    Sergei Izraelevich Gelfand ( Сергей Израилевич Г ельфанд) and Yuri Ivanovich Manin (Юрий Иванович Манин) .Methods of Ho- mological Algebra. Springer Monographs in Mathematics. Springer, Berlin, Germany, second edition, November 2002. doi:10.1007/ 978-3-662-12492-5

    2002

  56. [64]

    Hidden ghosts.Physics Letters B, 93(1–2):170–172, June 1980.doi:10.1016/0370-2693(80)90119-7

    Warren Siegel. Hidden ghosts.Physics Letters B, 93(1–2):170–172, June 1980.doi:10.1016/0370-2693(80)90119-7

    1980 doi

  57. [65]

    Quantum inequival- ence of different field representations.Physics Letters B, 94(2):179–182, July 1980.doi:10.1016/0370-2693(80)90852-7

    Michael James Duff and Peter van Nieuwenhuizen. Quantum inequival- ence of different field representations.Physics Letters B, 94(2):179–182, July 1980.doi:10.1016/0370-2693(80)90852-7

    1980 doi

  58. [66]

    Tyupkin (Юрий С

    Albert Solomonovich Schwarz (Альберт Соломонович Шварц) and Yuri S. Tyupkin (Юрий С. Тюпкин). Quantization of antisymmetric tensors and Ray–Singer torsion.Nuclear Physics B, 242:436–446, 1984. doi:10.1016/0550-3213(84)90403-6

    1984 doi

  59. [67]

    On 𝑆-duality in abelian gauge theory.Selecta Mathematica, 1(2):383–410, September 1995

    Edward Witten. On 𝑆-duality in abelian gauge theory.Selecta Mathematica, 1(2):383–410, September 1995. arXiv:hep-th/9505186, doi:10.1007/BF01671570

    1995 arXiv

  60. [68]

    Spin and Abelian electromagnetic duality on four-manifolds.Communications in Mathematical Physics, 217(2):331–356, March 2001

    David Ian Olive and Marcos Álvarez. Spin and Abelian electromagnetic duality on four-manifolds.Communications in Mathematical Physics, 217(2):331–356, March 2001. arXiv:hep-th/0003155, doi:10.1007/ s002200000354

    2001 arXiv

  61. [69]

    Donnelly, Benjamin Lewis Michel, and Aron Clark Wall

    William D. Donnelly, Benjamin Lewis Michel, and Aron Clark Wall. Electromagneticdualityandentanglementanomalies.PhysicalReviewD, 96(4):045008, 2017. arXiv:1611.05920, doi:10.1103/PhysRevD.96. 045008

    2017 arXiv

  62. [70]

    Odd di- mensional analogue of the Euler characteristic.Journal of High Energy Physics, 2021(12):178, December 2021

    Leron Borsten, Michael James Duff, and Silvia Nagy. Odd di- mensional analogue of the Euler characteristic.Journal of High Energy Physics, 2021(12):178, December 2021. arXiv:2105.13268, doi:10.1007/JHEP12(2021)178. 58

    2021 arXiv

  63. [71]

    Duality anomalies in linearized gravity

    Leron Borsten, Michael James Duff, Dimitri Kanakaris Decavel, and Hyungrok Kim (金炯錄). Duality anomalies in linearized gravity. Physical Review D, 2025.arXiv:2504.15973,doi:10.1103/3nkh-t15m

    2025 arXiv

  64. [72]

    Off-shell color-kinematics duality for Chern-Simons.Journal of High Energy Physics, 2022(08):035, August 2022.arXiv:2112.11452,doi:10.1007/JHEP08(2022)035

    Maor Ben-Shahar and Henrik Johansson. Off-shell color-kinematics duality for Chern-Simons.Journal of High Energy Physics, 2022(08):035, August 2022.arXiv:2112.11452,doi:10.1007/JHEP08(2022)035

    2022 arXiv

  65. [73]

    Kinematic Lie algebras from twistor spaces.Physical Review Letters, 131(4):041603, July 2023

    Leron Borsten, Branislav Jurco, Hyungrok Kim (金炯錄), Tommaso Macrelli, Christian Saemann, and Martin Wolf. Kinematic Lie algebras from twistor spaces.Physical Review Letters, 131(4):041603, July 2023. arXiv:2211.13261,doi:10.1103/PhysRevLett.131.041603

    2023 arXiv

  66. [74]

    Tree-levelcolor-kinematics duality from pure spinor actions.Physical Review D, 108(12):126012, December 2023

    Leron Borsten, Branislav Jurco, Hyungrok Kim (金炯錄), Tommaso Macrelli,ChristianSämann,andMartinWolf. Tree-levelcolor-kinematics duality from pure spinor actions.Physical Review D, 108(12):126012, December 2023. arXiv:2303.13596, doi:10.1103/PhysRevD.108. 126012

    2023 arXiv

  67. [75]

    Adjusted parallel transport for higher gauge theories.Journal of Physics A, 53(44):445206, November 2020.arXiv:1911.06390, doi:10.1088/1751-8121/ab8ef2

    Hyungrok Kim (金炯錄) and Christian Sämann. Adjusted parallel transport for higher gauge theories.Journal of Physics A, 53(44):445206, November 2020.arXiv:1911.06390, doi:10.1088/1751-8121/ab8ef2

    2020 arXiv

  68. [76]

    Lower-form symmetries, November 2022

    Thomas Vandermeulen. Lower-form symmetries, November 2022. arXiv:2211.04461,doi:10.48550/arXiv.2211.04461

    2022 doi arXiv

  69. [77]

    Heckman, Max Hübner, and Chitraang Murdia

    Jonathan J. Heckman, Max Hübner, and Chitraang Murdia. On the holographic dual of a topological symmetry operator.Phys. Rev. D, 110(4):046007, 2024. arXiv:2401.09538, doi:10.1103/PhysRevD.110. 046007

    2024 arXiv

  70. [78]

    Leonardo Santilli and Richard J. Szabo. Higher form symmet- ries and orbifolds of two-dimensional Yang–Mills theory.Lett. Math. Phys., 115(1):15, 2025. arXiv:2403.03119, doi:10.1007/ s11005-025-01905-4

    2025 arXiv

  71. [79]

    ( −1)-form symmetries from M-theory and SymTFTs.JHEP, 03:134, 2025

    Marwan Najjar, Leonardo Santilli, and Yi-Nan Wang. ( −1)-form symmetries from M-theory and SymTFTs.JHEP, 03:134, 2025. arXiv:2411.19683,doi:10.1007/JHEP03(2025)134

    2025 arXiv

  72. [80]

    Springer, New York City, New York, United States of America, second edition, September 1998

    Leslie Saunders Mac Lane.Categories for the Working Mathematician, volume 5 ofGraduate Texts in Mathematics. Springer, New York City, New York, United States of America, second edition, September 1998. doi:10.1007/978-1-4757-4721-8

    1998 doi

  73. [81]

    A nonabelian duality for (higher) gauge theories.Advances in Theoretical and Mathematical Physics, 25(1):241–274, 2021

    Ján Pulmann, Pavol Ševera, and Fridrich Valach. A nonabelian duality for (higher) gauge theories.Advances in Theoretical and Mathematical Physics, 25(1):241–274, 2021. arXiv:1909.06151, doi:10.4310/ATMP. 2021.v25.n1.a5. 59

    2021 arXiv

  74. [82]

    Schroeder.An Introduction to Quantum Field Theory

    Michael Edward Peskin and Daniel V. Schroeder.An Introduction to Quantum Field Theory. The Advanced Book Program. Perseus Books, Reading, Massachusetts, United States of America, 1995.doi: 10.1201/9780429503559

    1995 doi

  75. [83]

    Becchi-Rouet-Stora- Tyutin-Lagrangian double copy of Yang-Mills theory.Physical Review Letters, 126(19):191601, May 2021

    Leron Borsten, Branislav Jurčo, Hyungrok Kim (金炯錄), Tommaso Macrelli, Christian Sämann, and Martin Wolf. Becchi-Rouet-Stora- Tyutin-Lagrangian double copy of Yang-Mills theory.Physical Review Letters, 126(19):191601, May 2021. arXiv:2007.13803, doi:10.1103/ PhysRevLett.126.191601

    2021 arXiv

  76. [84]

    Double copy from homotopy algebras.Fortschritte der Physik, 69(8-9):2100075, 2021.arXiv: 2102.11390,doi:10.1002/prop.202100075

    Leron Borsten, Hyungrok Kim (金炯錄), Branislav Jurčo, Tommaso Macrelli, Christian Sämann, and Martin Wolf. Double copy from homotopy algebras.Fortschritte der Physik, 69(8-9):2100075, 2021.arXiv: 2102.11390,doi:10.1002/prop.202100075

    2021 arXiv

  77. [85]

    Monopoles, Dirac strings and generalised symmetries,November2024

    Christopher Michael Hull. Monopoles, Dirac strings and generalised symmetries,November2024. arXiv:2411.18741, doi:10.48550/arXiv. 2411.18741

    doi arXiv

  78. [86]

    Nguy˜ên, Tin Sulejmanpašić, and Mithat Ünsal

    Mendel T. Nguy˜ên, Tin Sulejmanpašić, and Mithat Ünsal. Phases of theories withℤ𝑁 1-form symmetry, and the roles of center vortices and magnetic monopoles.Physical Review Letters, 134(14):141902, April 2025. arXiv:2401.04800,doi:10.1103/PhysRevLett.134.141902

    2025 arXiv

  79. [87]

    TheStueckelbergfield.International Journal of Modern Physics A, 19(20):3265–3348, August 2004.arXiv: hep-th/0304245,doi:10.1142/S0217751X04019755

    HenriRueggandMartíRuiz-Altaba. TheStueckelbergfield.International Journal of Modern Physics A, 19(20):3265–3348, August 2004.arXiv: hep-th/0304245,doi:10.1142/S0217751X04019755

    2004 arXiv

  80. [88]

    Externalsourcesinfield–antifieldformalism.InternationalJournal of Modern Physics A, 29(10):1450058, April 2014

    Igor Anatolievich Batalin (Игорь Анатольевич Баталин) and Klaus Bering. Externalsourcesinfield–antifieldformalism.InternationalJournal of Modern Physics A, 29(10):1450058, April 2014. arXiv:1311.3653, doi:10.1142/S0217751X14500584

    2014 arXiv

  81. [89]

    Twistedhomotopyalgebras: Supersymmet- ric twists, spontaneous symmetry breaking, anomalies and localisation, August 2025.arXiv:2508.05134,doi:10.48550/arXiv.2508.05134

    LeronBorsten, DavidSimonHenrikJonsson, DimitriKanakarisDecavel, andHyungrokKim( 金炯錄). Twistedhomotopyalgebras: Supersymmet- ric twists, spontaneous symmetry breaking, anomalies and localisation, August 2025.arXiv:2508.05134,doi:10.48550/arXiv.2508.05134

    2025 doi

  82. [90]

    Michael C. Ogilvie. Phases of gauge theories.Journal of Phys- ics A, 45(48):483001, December 2012.arXiv:1211.2843, doi:10.1088/ 1751-8113/45/48/483001

    2012 arXiv

  83. [91]

    The center sym- metry and its spontaneous breakdown at high temperatures

    Kieran Michael Holland and Uwe-Jens Wiese. The center sym- metry and its spontaneous breakdown at high temperatures. In Mikhail Arkadyevich Shifman (Михаил Аркадьевич Шифман) , ed- itor,At the Frontier of Particle Physics. Boris Ioffe Festschrift, pages 1909– 1944, Singapore, ...

    1909 arXiv

  84. [92]

    Theory of one- and two-dimensional magnets with an easy magnetization plane

    Jacques Villain. Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet.Le Journal de Physique, 36(6):581–590, June 1975.doi:10.1051/ jphys:01975003606058100

    1975

  85. [93]

    CRC Press, Boca Raton, Florida, United States of America, second edition, 2003

    Mikio Nakahara (中原幹夫).Geometry, Topology and Physics. CRC Press, Boca Raton, Florida, United States of America, second edition, 2003. doi:10.1201/9781315275826

    2003 doi

  86. [94]

    SpringerStudium Mathematik – Master

    Torsten Wedhorn.Manifolds, Sheaves, andCohomology. SpringerStudium Mathematik – Master. Springer Spektrum, Wiesbaden, Germany, July 2016.doi:10.1007/978-3-658-10633-1

    2016 doi

  87. [95]

    Fibre Bundles, Topology and Gauge Fields

    Gerd Rudolph and Matthias Schmidt.Differential Geometry and Mathem- atical Physics: Part II. Fibre Bundles, Topology and Gauge Fields. Theoretical andMathematicalPhysics. Springer,Dordrecht,theNetherlands,March 2017.doi:10.1007/978-94-024-0959-8

    2017 doi

  88. [96]

    An invitation to higher gauge theory.General Relativity and Gravitation, 43(9):2335–2392, September 2011.arXiv:1003.4485,doi:10.1007/s10714-010-1070-9

    John Carlos Baez and John Huerta. An invitation to higher gauge theory.General Relativity and Gravitation, 43(9):2335–2392, September 2011.arXiv:1003.4485,doi:10.1007/s10714-010-1070-9

    2011 arXiv

  89. [97]

    Higher gauge theory

    Leron Borsten, Mehran Jalali Farahani, Branislav Jurčo, Hyungrok Kim (金炯錄), Jiří Nárožný, Dominik Rist, Christian Sämann, and Martin Wolf. Higher gauge theory. In Richard Joseph Szabo and Martin Bojowald, editors,Encyclopedia of Mathematical Physics, volume 4, pages 159–185. A...

    2025 arXiv

  90. [98]

    In Bertfried Fauser, Jürgen Tolksdorf, and Eberhard Zeidler, edit- ors,Quantum Field Theory: Competitive Models, pages 303–424, Basel, Switzerland, December 2009

    Hisham Sati, Urs Schreiber, and James Dillon Stasheff.𝐿∞-algebra con- nections and applications toString- and Chern-Simons𝑛-transport. In Bertfried Fauser, Jürgen Tolksdorf, and Eberhard Zeidler, edit- ors,Quantum Field Theory: Competitive Models, pages 303–424, Basel, Switzer...

    2009 arXiv

  91. [99]

    Differential twisted Stringand Fivebranestructures.CommunicationsinMathematical Physics, 315(1):169–213, October 2012.arXiv:0910.4001, doi:10.1007/ s00220-012-1510-3

    Hisham Sati, Urs Schreiber, and James Dillon Stasheff. Differential twisted Stringand Fivebranestructures.CommunicationsinMathematical Physics, 315(1):169–213, October 2012.arXiv:0910.4001, doi:10.1007/ s00220-012-1510-3

    2012 arXiv

  92. [100]

    Towards an M5-brane model II: Metric string structures.Fortschritte der Physik, 68(8):2000051, August 2020.arXiv:1908.08086,doi:10.1002/prop.202000051

    Christian Sämann and Lennart Schmidt. Towards an M5-brane model II: Metric string structures.Fortschritte der Physik, 68(8):2000051, August 2020.arXiv:1908.08086,doi:10.1002/prop.202000051

    2020 arXiv

  93. [101]

    Twisted Weil algebras for the string Lie 2-algebra

    Lennart Schmidt. Twisted Weil algebras for the string Lie 2-algebra. Fortschritte der Physik, 67(8–9):1910016, August–September 2019.arXiv: 1903.02873,doi:10.1002/prop.201910016. 61

    2019 arXiv

  94. [102]

    arXiv: 2106.00108,doi:10.48550/arXiv.2106.00108

    Leron Borsten, Hyungrok Kim (金炯錄), and Christian Sämann.𝐸𝐿∞- algebras,generalizedgeometry,andtensorhierarchies,May2021. arXiv: 2106.00108,doi:10.48550/arXiv.2106.00108

    doi

  95. [103]

    Chern correspondence for higher principal bundles,October2023

    Roberto Téllez-Domínguez. Chern correspondence for higher principal bundles,October2023. arXiv:2310.12738, doi:10.48550/arXiv.2310. 12738

    doi arXiv

  96. [104]

    Adjusted connections I: Differential cocycles for principal groupoid bundles with connection, June 2024

    Simon-Raphael Fischer, Mehran Jalali Farahani, Hyungrok Kim (金 炯錄), and Christian Sämann. Adjusted connections I: Differential cocycles for principal groupoid bundles with connection, June 2024. arXiv:2406.16755,doi:10.48550/arXiv.2406.16755

    2024 doi arXiv

  97. [105]

    Principal 3-bundles with adjusted connections, May 2025

    Gianni Gagliardo, Christian Sämann, and Roberto Téllez-Domínguez. Principal 3-bundles with adjusted connections, May 2025. arXiv: 2505.13368,doi:10.48550/arXiv.2505.13368

    2025 doi

  98. [106]

    Explicit non- Abelian gerbes with connections, February 2022.arXiv:2203.00092, doi:10.48550/arXiv.2203.00092

    Dominik Rist, Christian Sämann, and Martin Wolf. Explicit non- Abelian gerbes with connections, February 2022.arXiv:2203.00092, doi:10.48550/arXiv.2203.00092

    2022 doi

  99. [107]

    The non-abelian self-dual string.Letters in Mathematical Physics, 110(5):1001–1042, May 2020

    Christian Sämann and Lennart Schmidt. The non-abelian self-dual string.Letters in Mathematical Physics, 110(5):1001–1042, May 2020. arXiv:1705.02353,doi:10.1007/s11005-019-01250-3

    2020 arXiv

  100. [108]

    Paolo Aschieri, Luigi Cantini, and Branislav Jurčo. Nonabelian bundle gerbes, their differential geometry and gauge theory.Communications in Mathematical Physics, 254:367–400, March 2005.arXiv:hep-th/0312154, doi:10.1007/s00220-004-1220-6

    2005 arXiv

  101. [109]

    Principal 2-bundles and their gauge 2-groups

    Christoph Wockel. Principal 2-bundles and their gauge 2-groups. Forum Mathematicum, 23(3):565–610, 2011. arXiv:0803.3692, doi: 10.1515/FORM.2011.020

    2011 arXiv

  102. [110]

    Four equivalent versions of nonabelian gerbes.Pacific Journal of Mathematics, 246(2):355–420, 2013

    Thomas Nikolaus and Konrad Waldorf. Four equivalent versions of nonabelian gerbes.Pacific Journal of Mathematics, 246(2):355–420, 2013. arXiv:1103.4815,doi:10.2140/pjm.2013.264.355

    2013 arXiv

  103. [111]

    A global perspective to connections on principal 2-bundles.Forum Mathematicum, 30(4):809–843, July 2018

    Konrad Waldorf. A global perspective to connections on principal 2-bundles.Forum Mathematicum, 30(4):809–843, July 2018. arXiv: 1608.00401,doi:10.1515/forum-2017-0097. 62

    2018 arXiv

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