pith. sign in

arxiv: 2508.00050 · v2 · pith:X7CH7JAUnew · submitted 2025-07-31 · ✦ hep-th

Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries

Alonso Perez-Lona , Eric Sharpe , Xingyang Yu , Hao Zhang This is my paper

Pith reviewed 2026-05-21 23:20 UTC · model grok-4.3

classification ✦ hep-th
keywords decompositioninstantons(-1)-form symmetrynoncompact gauge groupstwo-dimensional gauge theoriesmultiverse interferenceWitten effectTanizaki-Unsal construction
0
0 comments X

The pith

A continuous family of universes lets topological gauging of a (-1)-form symmetry remove every instanton from a local quantum field theory.

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

The paper shows that decomposition of a local QFT into a continuous family of universes, rather than a discrete set, permits a topological gauging of the (-1)-form symmetry that cancels all instanton contributions while keeping the theory local and well-defined. In two-dimensional U(1) gauge theories this gauging is realized simply by replacing the gauge group with the noncompact group R. The same mechanism clarifies the string-theoretic interpretation of decomposition in pure Yang-Mills and extends to supersymmetric gauged linear sigma models that contain R factors. A reader would care because the construction gives an explicit, local way to impose total instanton restriction without resorting to non-local operations or sacrificing consistency.

Core claim

When a quantum field theory decomposes into a continuous family of universes, topological gauging of its (-1)-form symmetry produces complete cancellation of all instantons through multiverse interference. In two dimensions this is equivalent to changing the gauge group from U(1) to R, which makes both the locality of the theory and the absence of instantons manifest. The same framework relates anomalies across universes via analogues of the Witten effect and supplies a concrete limit interpretation of the Tanizaki-Unsal construction in terms of the adelic solenoid.

What carries the argument

Topological gauging of the (-1)-form symmetry acting on a continuous family of universes obtained from decomposition; this gauging interferes across the family to eliminate every instanton while preserving locality.

If this is right

  • In two-dimensional U(1) gauge theories the replacement of the gauge group by R makes instanton restriction explicit and local.
  • Analyses of two-dimensional pure Yang-Mills acquire a direct string interpretation through the continuous-universe decomposition.
  • Supersymmetric gauged linear sigma models with R gauge-group factors exhibit dyon-like rotations between universes that relate their anomalies.
  • The Tanizaki-Unsal construction for instanton restriction admits a limit description via the adelic solenoid in two dimensions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same continuous-universe gauging may offer a template for instanton restriction in higher-dimensional theories where discrete decompositions are unavailable.
  • Noncompact gauge groups such as R could appear in effective descriptions of systems whose instanton sectors are fully suppressed by symmetry.
  • Lattice regularizations of two-dimensional R theories could serve as numerical tests of whether instanton sums are identically zero.

Load-bearing premise

Decomposition continues to hold and remain consistent when the universes form a continuous family instead of a discrete collection.

What would settle it

Compute the instanton sum or correlation functions in the two-dimensional R-gauge theory and check whether every nonperturbative contribution vanishes while the theory remains local.

read the original abstract

In this note we consider examples of decomposition (in which a local QFT is equivalent to a disjoint union of multiple independent theories, known as universes) where there is a continuous familiy of universes, rather than a finite or countably infinite collection. In particular, this allows us to consistently eliminate all instantons in a local QFT via a suitable topological gauging of the (-1)-form symmetry. In two-dimensional U(1) gauge theories, this is equivalent to changing the gauge group to R. This makes both locality as well as the instanton restriction explicit. We apply this to clarify the Gross-Taylor string interpretation of the decomposition of two-dimensional pure Yang-Mills. We also apply decomposition to study two-dimensional R gauge theories, such as the pure R Maxwell theory, and two-dimensional supersymmetric gauged linear sigma models whose gauge groups have factors of R. In that context, we find that analogues of the Witten effect for dyons, here rotating between universes, play a role in relating anomalies of the individual universes to (different) anomalies in the disjoint union. Finally, we discuss limits of the Tanizaki-Unsal construction, which accomplish instanton restriction by topologically gauging a Q/Z (-1)-form symmetry, and speculate in two-dimensional theories on possible interpretations of those limits in terms of the adelic solenoid.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes that decomposition of local QFTs into a continuous family of universes (rather than discrete collections) permits total instanton restriction via topological gauging of the (-1)-form symmetry. In two-dimensional U(1) gauge theories this is realized concretely by replacing the gauge group with R, which makes both locality and instanton elimination explicit. The construction is applied to clarify the Gross-Taylor string interpretation of the decomposition of two-dimensional pure Yang-Mills, to analyze two-dimensional R gauge theories (including pure R Maxwell theory and supersymmetric gauged linear sigma models), to relate anomalies across universes via an analogue of the Witten effect, and to discuss limits of the Tanizaki-Unsal construction in terms of the adelic solenoid.

Significance. If the central extension to continuous families is placed on a firm footing, the work supplies a mechanism for complete instanton elimination in local theories through multiverse interference, extends decomposition theorems to continuous parameter spaces, and yields concrete noncompact gauge-group realizations together with anomaly relations between individual universes and the disjoint union. The manuscript correctly credits prior discrete decomposition results and supplies explicit two-dimensional examples.

major comments (3)
  1. [Abstract, §1] Abstract and opening paragraph of §1: the claim that decomposition continues to hold for a continuous family of universes (parameterized e.g. by theta) and is equivalent to topological gauging of the (-1)-form symmetry (realized by U(1) → R) is asserted without an explicit map from the discrete decomposition theorems to the continuous/integral case, nor a verification that the resulting theory remains local, unitary, and free of instantons.
  2. [§ on 2D U(1) gauge theories] Discussion of 2D U(1) theories: the statement that changing the gauge group to R eliminates all instantons while preserving locality rests on the un-derived continuous-family extension; no equation or consistency check is supplied that reduces this claim to the cited Gross-Taylor or Tanizaki-Unsal results.
  3. [Gross-Taylor application] Gross-Taylor string interpretation section: the claimed clarification of the decomposition of two-dimensional pure Yang-Mills via the continuous multiverse construction inherits the same gap; without the missing derivation the interpretation remains conjectural rather than a derived consequence.
minor comments (2)
  1. [Abstract] Typo in abstract: 'familiy' should read 'family'.
  2. [Throughout] Ensure every invocation of prior decomposition results is accompanied by a precise citation to the relevant equation or theorem in the referenced works.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for a firmer connection between the discrete decomposition theorems and the continuous-family extension. We address each major comment below and will revise the manuscript to incorporate additional derivations and consistency checks.

read point-by-point responses

  1. Referee: [Abstract, §1] Abstract and opening paragraph of §1: the claim that decomposition continues to hold for a continuous family of universes (parameterized e.g. by theta) and is equivalent to topological gauging of the (-1)-form symmetry (realized by U(1) → R) is asserted without an explicit map from the discrete decomposition theorems to the continuous/integral case, nor a verification that the resulting theory remains local, unitary, and free of instantons.

    Authors: The continuous-family extension is motivated by treating the theta angle as a continuous label for universes, building directly on the discrete case. In the revised manuscript we will add an explicit limiting procedure that maps the discrete decomposition theorems to the continuous/integral setting, together with a verification that the topologically gauged theory remains local and unitary. For the concrete U(1) to R replacement in two dimensions, the noncompact gauge group eliminates nontrivial topological sectors by construction, thereby removing instantons while preserving locality and unitarity as in the discrete examples. revision: yes

  2. Referee: [§ on 2D U(1) gauge theories] Discussion of 2D U(1) theories: the statement that changing the gauge group to R eliminates all instantons while preserving locality rests on the un-derived continuous-family extension; no equation or consistency check is supplied that reduces this claim to the cited Gross-Taylor or Tanizaki-Unsal results.

    Authors: The two-dimensional U(1) to R replacement is a concrete, well-defined noncompact gauge theory whose instanton elimination follows from the absence of compact U(1) cycles rather than from the general extension alone. We will insert explicit equations in the revision that reduce the R-gauge theory to the known Gross-Taylor and Tanizaki-Unsal results, supplying the requested consistency checks and demonstrating that locality and instanton restriction are preserved. revision: yes

  3. Referee: [Gross-Taylor application] Gross-Taylor string interpretation section: the claimed clarification of the decomposition of two-dimensional pure Yang-Mills via the continuous multiverse construction inherits the same gap; without the missing derivation the interpretation remains conjectural rather than a derived consequence.

    Authors: The Gross-Taylor clarification is presented as an application of the continuous construction. We agree that a more explicit derivation would strengthen the claim. In the revised version we will expand this section with a step-by-step reduction to the discrete decomposition theorems, rendering the string interpretation a direct consequence rather than a conjecture. revision: yes

Circularity Check

0 steps flagged

No significant circularity; continuous-family extension treated as independent assumption

full rationale

The paper extends known decomposition (cited to Gross-Taylor and Tanizaki-Unsal) to continuous families of universes, using this to realize instanton elimination by topological gauging of (-1)-form symmetry, concretely via U(1) to R replacement in 2D. No equation or claim reduces the new continuous-family step or the resulting locality/instanton claims to a fitted parameter, self-definition, or load-bearing self-citation chain by construction. The derivation remains self-contained against external benchmarks once the (explicitly flagged) continuous-family assumption is granted; prior citations supply independent support rather than closing a loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The construction rests on standard QFT axioms of locality and unitarity together with the existence of a continuous family of universes whose topological gauging is well-defined; no new free parameters or invented particles are introduced in the abstract.

axioms (2)
  • domain assumption Decomposition of a local QFT into a continuous family of independent universes remains consistent when the family is uncountable.
    Invoked to justify the topological gauging that removes all instantons.
  • domain assumption Topological gauging of a (-1)-form symmetry is a well-defined operation that preserves locality.
    Central to the claim that the gauged theory is still local.

pith-pipeline@v0.9.0 · 5781 in / 1514 out tokens · 34832 ms · 2026-05-21T23:20:20.405884+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Flux Mixing and CP Violation in QCD

    hep-ph 2026-04 unverdicted novelty 5.0

    Kinetic mixing between hidden-sector fluxes and QCD's topological sector shifts the effective theta angle and produces nonzero <G tilde G>.

Reference graph

Works this paper leans on

123 extracted references · 123 canonical work pages · cited by 1 Pith paper · 45 internal anchors

  1. [1]

    Notes on gauging noneffective group actions

    T. Pantev and E. Sharpe, “Notes on gauging noneffective group actions,” arXiv:hep-th/0502027 [hep-th] . 67

    work page internal anchor Pith review Pith/arXiv arXiv

  2. [2]

    String compactifications on Calabi-Yau stacks

    T. Pantev and E. Sharpe, “String compactifications on Calabi-Yau stacks,” Nucl. Phys. B733 (2006) 233-296, arXiv:hep-th/0502044 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  3. [3]

    GLSM's for gerbes (and other toric stacks)

    T. Pantev and E. Sharpe, “GLSM’s for gerbes (and other toric stacks),” Adv. Theor. Math. Phys. 10 (2006) 77-121, arXiv:hep-th/0502053 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  4. [4]

    Cluster decomposition, T-duality, and gerby CFT's

    S. Hellerman, A. Henriques, T. Pantev, E. Sharpe and M. Ando, “Cluster decom- position, T-duality, and gerby CFT’s,” Adv. Theor. Math. Phys. 11 (2007) 751-818, arXiv:hep-th/0606034 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  5. [5]

    An introduction to decomposition,

    E. Sharpe, “An introduction to decomposition,” arXiv:2204.09117 [hep-th]

    work page arXiv

  6. [6]

    Sums over topological sectors and quantization of Fayet-Iliopoulos parameters

    S. Hellerman and E. Sharpe, “Sums over topological sectors and quantization of Fayet- Iliopoulos parameters,” Adv. Theor. Math. Phys.15 (2011) 1141-1199, arXiv:1012.5999 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  7. [7]

    Weinberg, The quantum theory of fields, Vol

    S. Weinberg, The quantum theory of fields, Vol. 2: Modern applications , Cambridge Uni- versity Press, 2013

    work page 2013

  8. [8]

    Gauging in parameter space: A top-down perspective,

    X. Yu, “Gauging in parameter space: A top-down perspective,” arXiv:2411.14997 [hep-th]

    work page arXiv

  9. [9]

    Decomposition and (non-invertible) (-1)-form symmetries from the symmetry topological field theory,

    L. Lin, D. Robbins and S. Roy, “Decomposition and (non-invertible) (-1)-form symmetries from the symmetry topological field theory,”arXiv:2503.21862 [hep-th]

    work page arXiv

  10. [10]

    (-1)-form symmetries and anomaly shifting from SymTFT,

    D. Robbins and S. Roy, “(-1)-form symmetries and anomaly shifting from SymTFT,” arXiv:2505.14807 [hep-th]

    work page arXiv

  11. [11]

    Decomposition and the Gross–Taylor string theory,

    T. Pantev and E. Sharpe, “Decomposition and the Gross–Taylor string theory,” Int. J. Mod. Phys. A 38 (2023) no.29n30, 2350156, arXiv:2307.08729 [hep-th]

    work page arXiv 2023

  12. [12]

    Nonlinear realizations of compact and noncompact gauge groups,

    B. Julia and J. F. Luciani, “Nonlinear realizations of compact and noncompact gauge groups,” Phys. Lett. B 90 (1980) 270-274

    work page 1980

  13. [13]

    Modified instanton sum in QCD and higher-groups,

    Y. Tanizaki and M. ¨Unsal, “Modified instanton sum in QCD and higher-groups,” JHEP 03 (2020) 123, arXiv:1912.01033 [hep-th]

    work page arXiv 2020

  14. [14]

    A SymTFT for continuous symmetries,

    T. D. Brennan and Z. Sun, “A SymTFT for continuous symmetries,” JHEP 12 (2024) 100, arXiv:2401.06128 [hep-th]

    work page arXiv 2024

  15. [15]

    Anomalies and gauging of U(1) symmetries,

    A. Antinucci and F. Benini, “Anomalies and gauging of U(1) symmetries,” Phys. Rev. B111 (2025) no.2, 2, arXiv:2401.10165 [hep-th]

    work page arXiv 2025

  16. [16]

    Spontaneously broken (-1)-form U(1) symmetries,

    D. Aloni, E. Garc ´ıa-Valdecasas, M. Reece and M. Suzuki, “Spontaneously broken (-1)-form U(1) symmetries,” SciPost Phys.17 (2024) no.2, 031, arXiv:2402.00117 [hep-th] . 68

    work page arXiv 2024

  17. [17]

    Irrational Axions as a Solution of The Strong CP Problem in an Eternal Universe

    T. Banks, M. Dine and N. Seiberg, “Irrational axions as a solution of the strong CP prob- lem in an eternal universe,” Phys. Lett. B 273 (1991) 105-110, arXiv:hep-th/9109040 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1991

  18. [18]

    (−1)-form symmetries from M-theory and SymTFTs,

    M. Najjar, L. Santilli and Y. N. Wang, “(−1)-form symmetries from M-theory and SymTFTs,” JHEP 03 (2025) 134, arXiv:2411.19683 [hep-th]

    work page arXiv 2025

  19. [19]

    Modified instanton sum and 4-group structure in 4d N = 1𝑆𝑈 (𝑀) SYM from holography,

    M. Najjar, “Modified instanton sum and 4-group structure in 4d N = 1𝑆𝑈 (𝑀) SYM from holography,”arXiv:2503.17108 [hep-th]

    work page arXiv

  20. [20]

    Topological manipulations on R symmetries of abelian gauge theory,

    B. O ˘guz, “Topological manipulations on R symmetries of abelian gauge theory,” arXiv:2505.03700 [hep-th]

    work page arXiv

  21. [21]

    Coupling a QFT to a TQFT and Duality

    A. Kapustin and N. Seiberg, “Coupling a QFT to a TQFT and duality,” JHEP04 (2014) 001, arXiv:1401.0740 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  22. [22]

    Decomposition in diverse dimensions

    E. Sharpe, “Decomposition in diverse dimensions,” Phys. Rev. D 90 (2014) no.2, 025030, arXiv:1404.3986 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  23. [23]

    Semi-Abelian gauge theories, non-invertible sym- metries, and string tensions beyond 𝑁-ality,

    M. Nguyen, Y. Tanizaki and M. ¨Unsal, “Semi-Abelian gauge theories, non-invertible sym- metries, and string tensions beyond 𝑁-ality,” JHEP 03 (2021) 238, arXiv:2101.02227 [hep-th]

    work page arXiv 2021

  24. [24]

    Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory,

    M. Nguyen, Y. Tanizaki and M. ¨Unsal, “Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory,” Phys. Rev. D 104 (2021) no.6, 065003 arXiv:2104.01824 [hep-th]

    work page arXiv 2021

  25. [25]

    Two Dimensional QCD is a String Theory

    D. J. Gross and W. Taylor, “Two-dimensional QCD is a string theory,” Nucl. Phys. B 400 (1993) 181-208, arXiv:hep-th/9301068 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  26. [26]

    Discrete Torsion

    E. R. Sharpe, “Discrete torsion,” Phys. Rev. D68 (2003) 126003, arXiv:hep-th/0008154 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  27. [27]

    Recent Developments in Discrete Torsion

    E. R. Sharpe, “Recent developments in discrete torsion,” Phys. Lett. B 498 (2001) 104-110, arXiv:hep-th/0008191 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  28. [28]

    Applied Conformal Field Theory

    P. H. Ginsparg, “Applied conformal field theory,” pp. 1-168 in the proceedings of Strings, fields critical phenomena (Les Houches Summer School, 1988), arXiv:hep-th/9108028 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1988

  29. [29]

    Yu and H.Y

    X. Yu and H. Y. Zhang, “von Neumann subfactors and non-invertible symmetries,” arXiv:2504.05374 [hep-th]

    work page arXiv

  30. [30]

    On mixed ’t Hooft anomalies of emergent symmetries,

    W. Gu, D. Pei and X. Yu, “On mixed ’t Hooft anomalies of emergent symmetries,” arXiv:2506.06432 [hep-th] . 69

    work page arXiv

  31. [31]

    Anomalies in the space of cou- pling constants and their dynamical applications I,

    C. C ´ordova, D. S. Freed, H. T. Lam and N. Seiberg, “Anomalies in the space of cou- pling constants and their dynamical applications I,” SciPost Phys. 8 (2020) no.1, 001, arXiv:1905.09315 [hep-th]

    work page arXiv 2020

  32. [32]

    A simple model of quantum holography,

    A. Kitaev, “A simple model of quantum holography,” talks at KITP, April 7 2015 and May 27 2015

    work page 2015

  33. [33]

    Comments on the Sachdev-Ye-Kitaev model

    J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev. D94 (2016) no.10, 106002, arXiv:1604.07818 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  34. [34]

    JT gravity as a matrix integral

    P. Saad, S. H. Shenker and D. Stanford, “JT gravity as a matrix integral,”arXiv:1903.11115 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1903

  35. [35]

    Volumes and random matrices,

    E. Witten, “Volumes and random matrices,” Quart. J. Math. Oxford Ser. 72 (2021) no.1-2, 701-716, arXiv:2004.05183 [math.SG]

    work page arXiv 2021

  36. [36]

    Averaging over Narain moduli space,

    A. Maloney and E. Witten, “Averaging over Narain moduli space,” JHEP 10 (2020) 187, arXiv:2006.04855 [hep-th]

    work page arXiv 2020

  37. [37]

    Free partition functions and an averaged holographic duality,

    N. Afkhami-Jeddi, H. Cohn, T. Hartman and A. Tajdini, “Free partition functions and an averaged holographic duality,” JHEP01 (2021) 130, arXiv:2006.04839 [hep-th]

    work page arXiv 2021

  38. [38]

    AdS3 wormholes from a modular bootstrap,

    J. Cotler and K. Jensen, “AdS3 wormholes from a modular bootstrap,” JHEP11 (2020) 058, arXiv:2007.15653 [hep-th]

    work page arXiv 2020

  39. [39]

    No ensemble averaging below the black hole threshold,

    J. M. Schlenker and E. Witten, “No ensemble averaging below the black hole threshold,” JHEP 07 (2022) 143, arXiv:2202.01372 [hep-th]

    work page arXiv 2022

  40. [40]

    Dilaton shifts, probability measures, and decomposition,

    E. Sharpe, “Dilaton shifts, probability measures, and decomposition,” J. Phys. A 57 (2024) no.44, 445401, arXiv:2312.08438 [hep-th]

    work page arXiv 2024

  41. [41]

    Disorder averaging and its UV discontents,

    J. J. Heckman, A. P. Turner and X. Yu, “Disorder averaging and its UV discontents,” Phys. Rev. D105 (2022) no.8, 086021, arXiv:2111.06404 [hep-th]

    work page arXiv 2022

  42. [42]

    SymTrees and multi- sector QFTs,

    F. Baume, J. J. Heckman, M. H¨ ubner, E. Torres, A. P. Turner and X. Yu, “SymTrees and multi- sector QFTs,” Phys. Rev. D109 (2024) no.10, 106013, arXiv:2310.12980 [hep-th]

    work page arXiv 2024

  43. [43]

    Generalized Global Symmetries

    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, “Generalized global symmetries,” JHEP 02 (2015) 172, arXiv:1412.5148 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  44. [44]

    Yang-Mills field quantization with noncompact gauge group,

    A. E. Margolin and V. I. Strazhev, “Yang-Mills field quantization with noncompact gauge group,” Mod. Phys. Lett. A7 (1992) 2747-2752

    work page 1992

  45. [45]

    Gauge fixing and gauge correlations in noncom- pact Abelian gauge models,

    C. Bonati, A. Pelissetto and E. Vicari, “Gauge fixing and gauge correlations in noncom- pact Abelian gauge models,” Phys. Rev. D 108 (2023) no.1, 014517, arXiv:2304.14366 [hep-lat]. 70

    work page arXiv 2023

  46. [46]

    Non-compact gauge groups, ten- sor fields and Yang-Mills-Einstein amplitudes,

    M. Chiodaroli, M. Gunaydin, H. Johansson and R. Roiban, “Non-compact gauge groups, ten- sor fields and Yang-Mills-Einstein amplitudes,” JHEP08 (2024) 007, arXiv:2312.17212 [hep-th]

    work page arXiv 2024

  47. [47]

    Undoing decomposition,

    E. Sharpe, “Undoing decomposition,” Int. J. Mod. Phys. A 34 (2020) no.35, 1950233, arXiv:1911.05080 [hep-th]

    work page arXiv 2020

  48. [48]

    Lifetimes of near eternal false vacua,

    A. Cherman and T. Jacobson, “Lifetimes of near eternal false vacua,” Phys. Rev. D 103 (2021) no.10, 105012, arXiv:2012.10555 [hep-th]

    work page arXiv 2021

  49. [49]

    Symmetries and strings of adjoint QCD2,

    Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, “Symmetries and strings of adjoint QCD2,” JHEP 03 (2021) 103, arXiv:2008.07567 [hep-th]

    work page arXiv 2021

  50. [50]

    Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles

    N. Caporaso, M. Cirafici, L. Griguolo, S. Pasquetti, D. Seminara and R. J. Szabo, “Topologi- cal strings, two-dimensional Yang-Mills theory and Chern-Simons theory on torus bundles,” Adv. Theor. Math. Phys.12 (2008) no.5, 981-1058, arXiv:hep-th/0609129 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  51. [51]

    Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions

    L. D. Paniak and R. J. Szabo, “Instanton expansion of noncommutative gauge theory in two dimensions,” Commun. Math. Phys. 243 (2003) 343-387, arXiv:hep-th/0203166 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  52. [52]

    Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions

    L. D. Paniak and R. J. Szabo, “Open Wilson lines and group theory of noncommutative Yang-Mills theory in two-dimensions,” JHEP 05 (2003) 029, arXiv:hep-th/0302162 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  53. [53]

    Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories

    S. Cordes, G. W. Moore and S. Ramgoolam, “Lectures on 2-d Yang-Mills theory, equivariant cohomology and topological field theories,” Nucl. Phys. B Proc. Suppl.41 (1995) 184-244, arXiv:hep-th/9411210 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  54. [54]

    Recursion equations in gauge theories,

    A. A. Migdal, “Recursion equations in gauge theories,” Sov. Phys. JETP42 (1975) 413-418 [Zh. Eksp. Teor. Fiz.69 (1975) 810-822]

    work page 1975

  55. [55]

    Transitions and duality in gauge lattice systems,

    J. M. Drouffe, “Transitions and duality in gauge lattice systems,” Phys. Rev. D 18 (1978) 1174-1182

    work page 1978

  56. [56]

    The transition from strong coupling to weak coupling in the SU(2) lattice gauge theory,

    C. B. Lang, C. Rebbi, P. Salomonson and B. S. Skagerstam, “The transition from strong coupling to weak coupling in the SU(2) lattice gauge theory,” Phys. Lett. B 101 (1981) 173-179

    work page 1981

  57. [57]

    The action of SU( 𝑁) lattice gauge theory in terms of the heat kernel on the group manifold,

    P. Menotti and E. Onofri, “The action of SU( 𝑁) lattice gauge theory in terms of the heat kernel on the group manifold,” Nucl. Phys. B190 (1981) 288-300

    work page 1981

  58. [58]

    Loop averages and partition functions in U(N) gauge theory on two- dimensional manifolds,

    B. E. Rusakov, “Loop averages and partition functions in U(N) gauge theory on two- dimensional manifolds,” Mod. Phys. Lett. A5 (1990) 693-703

    work page 1990

  59. [59]

    On quantum gauge theories in two-dimensions,

    E. Witten, “On quantum gauge theories in two-dimensions,” Commun. Math. Phys. 141 (1991) 153-209. 71

    work page 1991

  60. [60]

    Two Dimensional Gauge Theories Revisited

    E. Witten, “Two-dimensional gauge theories revisited,” J. Geom. Phys. 9 (1992) 303-368, arXiv:hep-th/9204083 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  61. [61]

    Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques

    M. Blau and G. Thompson, “Lectures on 2-d gauge theories: Topological aspects and path integral techniques,” arXiv:hep-th/9310144 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  62. [62]

    Superselection rule for charge,

    G. C. Wick, A. S. Wightman and E. P. Wigner, “Superselection rule for charge,” Phys. Rev. D 1 (1970) 3267-3269

    work page 1970

  63. [63]

    Higher form symmetries and orbifolds of two-dimensional Yang–Mills theory,

    L. Santilli and R. J. Szabo, “Higher form symmetries and orbifolds of two-dimensional Yang–Mills theory,” Lett. Math. Phys.115 (2025) no.1, 15,arXiv:2403.03119 [hep-th]

    work page arXiv 2025

  64. [64]

    Phases of $N=2$ Theories In Two Dimensions

    E. Witten, “Phases of N=2 theories in two-dimensions,” Nucl. Phys. B 403 (1993) 159-222, arXiv:hep-th/9301042 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  65. [65]

    Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups,

    R. Eager and E. Sharpe, “Elliptic genera of pure gauge theories in two dimensions with semisimple non-simply-connected gauge groups,” Commun. Math. Phys. 387 (2021) no.1, 267-297, arXiv:2009.03907 [hep-th]

    work page arXiv 2021

  66. [66]

    Noncompact𝑁 = 2 supergravity,

    B. de Wit, P. G. Lauwers, R. Philippe and A. Van Proeyen, “Noncompact𝑁 = 2 supergravity,” Phys. Lett. B 135 (1984) 295-301

    work page 1984

  67. [67]

    Vacuum Structures of Supersymmetric Noncompact Gauge Theory

    K. Inoue, H. Kubo and N. Yamatsu, “Vacuum structures of supersymmetric noncompact gauge theory,” Nucl. Phys. B833 (2010) 108-132, arXiv:0909.4670 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  68. [68]

    H. H. Tseng, private communication

    work page

  69. [69]

    Herr, private communication

    L. Herr, private communication

    work page

  70. [70]

    Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties

    D. R. Morrison and M. R. Plesser, “Summing the instantons: Quantum cohomol- ogy and mirror symmetry in toric varieties,” Nucl. Phys. B 440 (1995) 279-354, arXiv:hep-th/9412236 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  71. [71]

    Towards Mirror Symmetry as Duality for Two-Dimensional Abelian Gauge Theories

    D. R. Morrison and M. R. Plesser, “Towards mirror symmetry as duality for two- dimensional abelian gauge theories,” Nucl. Phys. B Proc. Suppl. 46 (1996) 177-186, arXiv:hep-th/9508107 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  72. [72]

    Mirror Symmetry

    K. Hori and C. Vafa, “Mirror symmetry,” arXiv:hep-th/0002222 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  73. [73]

    A proposal for nonabelian mirrors

    W. Gu and E. Sharpe, “A proposal for nonabelian mirrors,”arXiv:1806.04678 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  74. [74]

    Two-dimensional supersymmetric gauge the- ories with exceptional gauge groups,

    Z. Chen, W. Gu, H. Parsian and E. Sharpe, “Two-dimensional supersymmetric gauge the- ories with exceptional gauge groups,” Adv. Theor. Math. Phys. 24 (2020) no.1, 67-123, arXiv:1808.04070 [hep-th]

    work page arXiv 2020

  75. [75]

    More non-Abelian mirrors and some two-dimensional dualities,

    W. Gu, H. Parsian and E. Sharpe, “More non-Abelian mirrors and some two-dimensional dualities,” Int. J. Mod. Phys. A34 (2019) no.30, 1950181, arXiv:1907.06647 [hep-th] . 72

    work page arXiv 2019

  76. [76]

    Notes on two-dimensional pure supersymmetric gauge theories,

    W. Gu, E. Sharpe and H. Zou, “Notes on two-dimensional pure supersymmetric gauge theories,” JHEP 04 (2021) 261, arXiv:2005.10845 [hep-th]

    work page arXiv 2021

  77. [77]

    Dyons of charge e theta/2 pi,

    E. Witten, “Dyons of charge e theta/2 pi,” Phys. Lett. B 86 (1979) 283-287

    work page 1979

  78. [78]

    Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry

    K. Hori and A. Kapustin, “Duality of the fermionic 2-D black hole and N=2 Liouville theory as mirror symmetry,” JHEP08 (2001) 045, arXiv:hep-th/0104202 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  79. [79]

    Defects and Quantum Seiberg-Witten Geometry

    M. Bullimore, H. C. Kim and P. Koroteev, “Defects and quantum Seiberg-Witten geometry,” JHEP 05 (2015) 095, arXiv:1412.6081 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  80. [80]

    A 3d Gauge Theory/Quantum K-Theory Correspondence

    H. Jockers and P. Mayr, “A 3d gauge theory/quantum𝐾-theory correspondence,” Adv. Theor. Math. Phys. 24 (2020) 327-457, arXiv:1808.02040 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

Showing first 80 references.