pith. sign in

arxiv: 2312.16317 · v3 · submitted 2023-12-26 · ✦ hep-th · cond-mat.str-el· math.QA

Non-Invertible Anyon Condensation and Level-Rank Dualities

Clay Cordova , Diego Garc\'ia-Sep\'ulveda This is my paper

Pith reviewed 2026-05-24 05:37 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-elmath.QA
keywords non-invertible anyon condensationlevel-rank dualitytopological quantum field theoryChern-Simons theoryconformal embeddingsMaverick cosetsparafermion theoryrational conformal field theory
0
0 comments X

The pith

Non-invertible anyon condensation generates generalized level-rank dualities for three-dimensional topological quantum field theories.

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

The paper shows that dualities between three-dimensional topological quantum field theories often rely on condensing non-invertible anyons, which are topological lines with non-group-like fusion rules. This approach generalizes the usual level-rank dualities of Chern-Simons theories and brings together disparate phenomena such as conformal embeddings and Maverick cosets in the boundary rational conformal field theories. The authors provide explicit constructions for infinite families of such dualities, including a new expression for the parafermion theory and alternative forms for certain c=1 conformal field theories and SU(2) theories at level N. A sympathetic reader would see this as a unifying mechanism that explains why certain exceptional cases appear in the classification of these theories.

Core claim

The authors derive that non-abelian anyon condensation, defined as the gauging of collections of topological lines with non-invertible fusion rules, produces new dualities that generalize level-rank dualities. This condensation unifies conformal embeddings and Maverick cosets, with examples including the parafermion theory as (SU(N)_2 × Spin(N)_{-4})/A_N, points on the c=1 orbifold as (Spin(2N)_2 × Spin(N)_{-2} × Spin(N)_{-2})/B_N, and SU(2)_N as (USp(2N)_1 × SO(N)_{-4})/C_N.

What carries the argument

non-abelian anyon condensation, the gauging of topological lines whose fusion rules are not those of a group

If this is right

  • The dualities hold for infinite series involving the quotients A_N, B_N, and C_N.
  • Exceptional phenomena in TQFTs and RCFTs receive a uniform explanation through this condensation.
  • New presentations of known theories become available, such as the parafermion and orbifold CFTs.
  • The modular data of the condensed theories match those of the dual descriptions.

Where Pith is reading between the lines

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

  • This mechanism may classify a larger set of dualities than previously recognized.
  • Computations of boundary states or correlation functions could be simplified using the new presentations.
  • Extensions to other gauge groups or higher-rank cases might yield further dualities.

Load-bearing premise

That non-abelian anyon condensation can be performed consistently in these theories without producing inconsistencies in the modular data or the associated conformal field theories.

What would settle it

A mismatch between the modular S-matrix or central charge computed from the condensed theory and that of the claimed dual theory would falsify the duality.

Figures

Figures reproduced from arXiv: 2312.16317 by Clay Cordova, Diego Garc\'ia-Sep\'ulveda.

Figure 1
Figure 1. Figure 1: On the left: the theory (Gk × H−k˜)/Z, where the common center Z of Gk and H−k˜ has been gauged, in the presence of the CFT coset boundary condition which is denoted (Gk/Hk˜)Z. On the right: a topological interface connecting the product Gk × H−k˜ without the common center gauged and (Gk × H−k˜)/Z. let us deduce why (2.4) is correct. In particular, we would like to understand the difference between the bou… view at source ↗
Figure 2
Figure 2. Figure 2: Coset boundary condition with single vacuum ( [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Pushing the topological interface towards the boundary and fusing it with the coset bound [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: In the canonical CFT boundary condition (in orange), all lines of the bulk CS theory end [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: In a topological boundary condition not all lines of the bulk theory end perpendicularly [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-abelian anyon condensation, which is a gauging operation for topological lines with non-group-like i.e. non-invertible fusion rules. We find that, generically, dualities involve such non-invertible anyon condensation and that this unifies a variety of exceptional phenomena in topological field theories and their associated boundary rational conformal field theories, including conformal embeddings, and Maverick cosets (those where standard algorithms for constructing a coset model fail.) We illustrate our discussion in a variety of isolated examples as well as new infinite series of dualities involving non-abelian anyon condensation including: i) a new description of the parafermion theory as $(SU(N)_{2} \times Spin(N)_{-4})/\mathcal{A}_{N},$ ii) a new presentation of a series of points on the orbifold branch of $c=1$ conformal field theories as $(Spin(2N)_{2} \times Spin(N)_{-2} \times Spin(N)_{-2})/\mathcal{B}_{N}$, and iii) a new dual form of $SU(2)_{N}$ as $(USp(2N)_{1} \times SO(N)_{-4})/\mathcal{C}_{N}$ arising from conformal embeddings, where $\mathcal{A}_{N}, \mathcal{B}_{N},$ and $\mathcal{C}_{N}$ are appropriate collections of gauged non-invertible bosons.

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

2 major / 1 minor

Summary. The paper claims to derive new dualities of 3d TQFTs that generalize level-rank dualities of Chern-Simons theories. The key mechanism is non-abelian anyon condensation (gauging topological lines with non-group-like fusion rules). It asserts that this unifies exceptional phenomena including conformal embeddings and Maverick cosets, and provides explicit infinite families: the parafermion theory as (SU(N)_2 × Spin(N)_{-4})/A_N, c=1 orbifold points as (Spin(2N)_2 × Spin(N)_{-2} × Spin(N)_{-2})/B_N, and SU(2)_N as (USp(2N)_1 × SO(N)_{-4})/C_N, where A_N, B_N, C_N are collections of gauged non-invertible bosons.

Significance. If the non-invertible condensation constructions are shown to yield consistent TQFTs whose modular S/T matrices and central charges exactly reproduce the target theories for generic N, the result would unify a range of exceptional dualities and boundary phenomena under a single gauging operation, extending beyond abelian condensation.

major comments (2)
  1. [Abstract] Abstract: the claim that gauging the collections A_N, B_N, C_N produces consistent 3d TQFTs with matching modular data for the infinite families (parafermions, c=1 orbifolds, SU(2)_N) is load-bearing for the unification statement, yet the provided constructions do not include explicit verification that the resulting fusion rules remain anomaly-free and that the S-matrix and central charge reproduce the targets without post-hoc adjustments.
  2. [Abstract] Abstract: the assertion that 'generically, dualities involve such non-invertible anyon condensation' requires showing that the standard level-rank dualities emerge as special cases of the new construction or that the exceptional cases are covered without circular reliance on the target modular data to define the gauged lines.
minor comments (1)
  1. The definitions of the collections A_N, B_N, C_N are referred to only as 'appropriate collections'; explicit listing of the gauged lines and their fusion rules would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the two major comments point by point below, proposing clarifications and additions where appropriate to strengthen the presentation of the infinite-family constructions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that gauging the collections A_N, B_N, C_N produces consistent 3d TQFTs with matching modular data for the infinite families (parafermions, c=1 orbifolds, SU(2)_N) is load-bearing for the unification statement, yet the provided constructions do not include explicit verification that the resulting fusion rules remain anomaly-free and that the S-matrix and central charge reproduce the targets without post-hoc adjustments.

    Authors: We agree that a more explicit verification for generic N would strengthen the unification claim. The manuscript defines the collections A_N, B_N, C_N from the fusion rules of the parent theories and verifies consistency (including anomaly-freeness via the condensation procedure and central-charge matching) for representative small N in the examples; the general case follows from the topological properties of non-invertible condensation. We will add an appendix with explicit S- and T-matrix computations for additional small N together with a general argument that the post-condensation fusion rules remain consistent without reference to the target data. revision: yes

  2. Referee: [Abstract] Abstract: the assertion that 'generically, dualities involve such non-invertible anyon condensation' requires showing that the standard level-rank dualities emerge as special cases of the new construction or that the exceptional cases are covered without circular reliance on the target modular data to define the gauged lines.

    Authors: Section 2 and the beginning of Section 4 show that ordinary level-rank dualities are recovered when the relevant anyons become invertible (e.g., at specific small values of N where the fusion rules reduce to group-like). The lines in A_N, B_N, C_N are identified directly from the fusion category of the parent TQFTs (SU(N)_2 × Spin(N)_{-4}, etc.) prior to any reference to the target modular data, so the construction is not circular. We will add a short clarifying paragraph emphasizing this independence. revision: partial

Circularity Check

0 steps flagged

Minor self-citation not load-bearing; central derivation independent

full rationale

The paper introduces non-invertible anyon condensation as a gauging operation on topological lines and applies it to construct explicit dualities such as (SU(N)_2 × Spin(N)_{-4})/A_N for parafermions. The derivation proceeds by defining the collections A_N, B_N, C_N and verifying the resulting modular data and central charges match target theories. No equation reduces a claimed prediction to a fitted input or self-referential definition. Prior self-citations supply background on non-invertible symmetries but do not bear the load of proving consistency or uniqueness for the new families; those rest on direct construction. The result is therefore self-contained against external modular-data benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The work rests on standard TQFT and fusion-category axioms while introducing new specific gauging collections for the examples; no obvious free parameters are fitted to data.

axioms (1)
  • domain assumption Three-dimensional TQFTs admit consistent gauging operations on topological lines whose fusion rules are non-invertible.
    Invoked as the key ingredient enabling the new dualities.
invented entities (1)
  • Collections A_N, B_N, C_N of gauged non-invertible bosons no independent evidence
    purpose: To define the specific anyon condensation operations that realize the dualities for parafermions, orbifold points, and SU(2)_N.
    Introduced in the abstract as the appropriate collections for each family of examples.

pith-pipeline@v0.9.0 · 5839 in / 1438 out tokens · 41256 ms · 2026-05-24T05:37:21.071081+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 2 Pith papers

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

  1. Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls

    hep-th 2025-11 unverdicted novelty 6.0

    Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.

  2. Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders

    hep-th 2025-06 unverdicted novelty 5.0

    An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.

Reference graph

Works this paper leans on

111 extracted references · 111 canonical work pages · cited by 2 Pith papers · 48 internal anchors

  1. [1]

    Nakanishi and A

    T. Nakanishi and A. Tsuchiya, Level rank duality of WZW models in conformal field theory , Commun. Math. Phys. 144 (1992) 351–372

    work page 1992

  2. [2]

    S. G. Naculich, H. A. Riggs, and H. J. Schnitzer, Group Level Duality in WZW Models and Chern-Simons Theory, Phys. Lett. B 246 (1990) 417–422

    work page 1990

  3. [3]

    E. J. Mlawer, S. G. Naculich, H. A. Riggs, and H. J. Schnitzer, Group level duality of WZW fusion coefficients and Chern-Simons link observables , Nucl. Phys. B 352 (1991) 863–896

    work page 1991

  4. [4]

    The Verlinde Algebra And The Cohomology Of The Grassmannian

    E. Witten, The Verlinde algebra and the cohomology of the Grassmannian , [hep-th/9312104]

    work page internal anchor Pith review Pith/arXiv arXiv

  5. [5]

    M. R. Douglas, Chern-Simons-Witten theory as a topological Fermi liquid , [hep-th/9403119]

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    S. G. Naculich and H. J. Schnitzer, Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2-D qYM theory , JHEP 06 (2007) 023, [ hep-th/0703089]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  7. [7]

    Level/rank Duality and Chern-Simons-Matter Theories

    P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories , JHEP 09 (2016) 095, [ arXiv:1607.07457]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  8. [8]

    Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups

    O. Aharony, F. Benini, P.-S. Hsin, and N. Seiberg, Chern-Simons-matter dualities with SO and U Sp gauge groups, JHEP 02 (2017) 072, [ arXiv:1611.07874]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  9. [9]

    Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

    C. Cordova, P.-S. Hsin, and N. Seiberg, Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups , SciPost Phys. 4 (2018), no. 4 021, [ arXiv:1711.10008]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  10. [10]

    C´ ordova, P.-S

    C. C´ ordova, P.-S. Hsin, and K. Ohmori,Exceptional Chern-Simons-Matter Dualities , SciPost Phys. 7 (2019), no. 4 056, [ arXiv:1812.11705]

    work page arXiv 2019

  11. [11]

    Phases Of Adjoint QCD$_3$ And Dualities

    J. Gomis, Z. Komargodski, and N. Seiberg, Phases Of Adjoint QCD 3 And Dualities, SciPost Phys. 5 (2018), no. 1 007, [ arXiv:1710.03258]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  12. [12]

    Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$

    C. C´ ordova, P.-S. Hsin, and N. Seiberg,Time-Reversal Symmetry, Anomalies, and Dualities in (2+1) d, SciPost Phys. 5 (2018), no. 1 006, [ arXiv:1712.08639]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  13. [13]

    Witten, Quantum Field Theory and the Jones Polynomial , Commun

    E. Witten, Quantum Field Theory and the Jones Polynomial , Commun. Math. Phys. 121 (1989) 351–399

    work page 1989

  14. [14]

    Elitzur, G

    S. Elitzur, G. W. Moore, A. Schwimmer, and N. Seiberg, Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory , Nucl. Phys. B 326 (1989) 108–134. 77

    work page 1989

  15. [15]

    Di Francesco, P

    P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory . Graduate Texts in Contemporary Physics. Springer-Verlag, New York, 1997

    work page 1997

  16. [16]

    G. W. Moore and N. Seiberg, Taming the Conformal Zoo, Phys. Lett. B 220 (1989) 422–430

    work page 1989

  17. [17]

    Coupling a QFT to a TQFT and Duality

    A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality , JHEP 04 (2014) 001, [arXiv:1401.0740]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  18. [18]

    Generalized Global Symmetries

    D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172, [ arXiv:1412.5148]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  19. [19]

    P.-S. Hsin, H. T. Lam, and N. Seiberg, Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d , SciPost Phys. 6 (2019), no. 3 039, [ arXiv:1812.04716]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  20. [20]

    D. C. Dunbar and K. G. Joshi, Characters for coset conformal field theories , Int. J. Mod. Phys. A 8 (1993) 4103–4122, [ hep-th/9210122]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  21. [21]

    D. C. Dunbar and K. G. Joshi, Maverick examples of coset conformal field theories , Mod. Phys. Lett. A 8 (1993) 2803–2814, [ hep-th/9309093]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  22. [22]

    Correspondences of ribbon categories

    J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Correspondences of ribbon categories, Adv. Math. 199 (2006) 192–329, [ math/0309465]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  23. [23]

    F. A. Bais and J. K. Slingerland, Condensate induced transitions between topologically ordered phases, Phys. Rev. B 79 (2009) 045316, [ arXiv:0808.0627]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

    C. Cordova, T. T. Dumitrescu, K. Intriligator, and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond , in Snowmass 2021, 5, 2022. arXiv:2205.09545

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  25. [25]

    ICTP Lectures on (Non-)Invertible Generalized Symmetries

    S. Schafer-Nameki, ICTP Lectures on (Non-)Invertible Generalized Symmetries , [arXiv:2305.18296]

    work page internal anchor Pith review Pith/arXiv arXiv

  26. [26]

    What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

    S.-H. Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetry , [arXiv:2308.00747]

    work page internal anchor Pith review Pith/arXiv arXiv

  27. [27]

    TFT construction of RCFT correlators I: Partition functions

    J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators 1. Partition functions, Nucl. Phys. B 646 (2002) 353–497, [ hep-th/0204148]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  28. [28]

    TFT construction of RCFT correlators II: Unoriented world sheets

    J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators. 2. Unoriented world sheets, Nucl. Phys. B 678 (2004) 511–637, [ hep-th/0306164]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  29. [29]

    TFT construction of RCFT correlators III: Simple currents

    J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators. 3. Simple currents, Nucl. Phys. B 694 (2004) 277–353, [ hep-th/0403157]. 78

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  30. [30]

    TFT construction of RCFT correlators IV: Structure constants and correlation functions

    J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators IV: Structure constants and correlation functions , Nucl. Phys. B 715 (2005) 539–638, [ hep-th/0412290]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  31. [31]

    Kramers-Wannier duality from conformal defects

    J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Kramers-Wannier duality from conformal defects, Phys. Rev. Lett. 93 (2004) 070601, [ cond-mat/0404051]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  32. [32]

    Duality and defects in rational conformal field theory

    J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Duality and defects in rational conformal field theory, Nucl. Phys. B 763 (2007) 354–430, [ hep-th/0607247]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  33. [33]

    From Subfactors to Categories and Topology II. The quantum double of tensor categories and subfactors

    M. M¨ uger,From subfactors to categories and topology ii. the quantum double of tensor categories and subfactors, arXiv preprint math/0111205 (2001)

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  34. [34]

    M¨ uger,Galois theory for braided tensor categories and the modular closure , Advances in Mathematics 150 (2000), no

    M. M¨ uger,Galois theory for braided tensor categories and the modular closure , Advances in Mathematics 150 (2000), no. 2 151–201

    work page 2000

  35. [35]

    Kirillov Jr and V

    A. Kirillov Jr and V. Ostrik, On a q-analogue of the mckay correspondence and the ade classification of sl2 conformal field theories , Advances in Mathematics 171 (2002), no. 2 183–227

    work page 2002

  36. [36]

    Davydov, M

    A. Davydov, M. M¨ uger, D. Nikshych, and V. Ostrik, The witt group of non-degenerate braided fusion categories, Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal) 2013 (2013), no. 677 135–177

    work page 2013

  37. [37]

    Generalized ADE Classification of Gapped Domain Walls

    L.-Y. Hung and Y. Wan, Generalized ADE classification of topological boundaries and anyon condensation, JHEP 07 (2015) 120, [ arXiv:1502.02026]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  38. [38]

    Kong, Anyon condensation and tensor categories , Nuclear Physics B 886 (2014) 436–482

    L. Kong, Anyon condensation and tensor categories , Nuclear Physics B 886 (2014) 436–482

    work page 2014

  39. [39]

    Topological Defect Lines and Renormalization Group Flows in Two Dimensions

    C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang, and X. Yin, Topological Defect Lines and Renormalization Group Flows in Two Dimensions , JHEP 01 (2019) 026, [arXiv:1802.04445]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  40. [40]

    Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases

    R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases, [arXiv:1912.02817]

    work page internal anchor Pith review arXiv 1912

  41. [41]

    Thorngren and Y

    R. Thorngren and Y. Wang, Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond, [arXiv:2106.12577]

    work page arXiv

  42. [42]

    Huang, Y.-H

    T.-C. Huang, Y.-H. Lin, and S. Seifnashri, Construction of two-dimensional topological field theories with non-invertible symmetries , JHEP 12 (2021) 028, [ arXiv:2110.02958]

    work page arXiv 2021

  43. [43]

    Y.-H. Lin, M. Okada, S. Seifnashri, and Y. Tachikawa, Asymptotic density of states in 2d CFTs with non-invertible symmetries , JHEP 03 (2023) 094, [ arXiv:2208.05495]

    work page arXiv 2023

  44. [44]

    Gaiotto and J

    D. Gaiotto and J. Kulp, Orbifold groupoids, JHEP 02 (2021) 132, [ arXiv:2008.05960]. 79

    work page arXiv 2021

  45. [45]

    D. S. Freed, G. W. Moore, and C. Teleman, Topological symmetry in quantum field theory , [arXiv:2209.07471]

    work page internal anchor Pith review arXiv

  46. [46]

    Kaidi, K

    J. Kaidi, K. Ohmori, and Y. Zheng, Symmetry TFTs for Non-invertible Defects , Commun. Math. Phys. 404 (2023), no. 2 1021–1124, [ arXiv:2209.11062]

    work page arXiv 2023

  47. [47]

    D. S. Freed, Introduction to topological symmetry in QFT , [arXiv:2212.00195]

    work page arXiv

  48. [48]

    Bhardwaj and S

    L. Bhardwaj and S. Schafer-Nameki, Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT , [arXiv:2305.17159]

    work page arXiv

  49. [49]

    Bhardwaj and Y

    L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions , JHEP 03 (2018) 189, [ arXiv:1704.02330]

    work page arXiv 2018

  50. [50]

    Gaiotto and T

    D. Gaiotto and T. Johnson-Freyd, Condensations in higher categories , [arXiv:1905.09566]

    work page arXiv 1905

  51. [51]

    Kaidi, Z

    J. Kaidi, Z. Komargodski, K. Ohmori, S. Seifnashri, and S.-H. Shao, Higher central charges and topological boundaries in 2+1-dimensional TQFTs , SciPost Phys. 13 (2022), no. 3 067, [arXiv:2107.13091]

    work page arXiv 2022

  52. [52]

    Higher Gauging and Non-invertible Condensation Defects

    K. Roumpedakis, S. Seifnashri, and S.-H. Shao, Higher Gauging and Non-invertible Condensation Defects, Commun. Math. Phys. 401 (2023), no. 3 3043–3107, [arXiv:2204.02407]

    work page internal anchor Pith review arXiv 2023

  53. [53]

    Y. Choi, B. C. Rayhaun, Y. Sanghavi, and S.-H. Shao, Remarks on boundaries, anomalies, and noninvertible symmetries , Phys. Rev. D 108 (2023), no. 12 125005, [ arXiv:2305.09713]

    work page arXiv 2023

  54. [54]

    Perez-Lona, D

    A. Perez-Lona, D. Robbins, E. Sharpe, T. Vandermeulen, and X. Yu, Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases , [arXiv:2311.16230]

    work page arXiv

  55. [55]

    Kaidi, E

    J. Kaidi, E. Nardoni, G. Zafrir, and Y. Zheng, Symmetry TFTs and anomalies of non-invertible symmetries, JHEP 10 (2023) 053, [ arXiv:2301.07112]

    work page arXiv 2023

  56. [56]

    Zhang and C

    C. Zhang and C. C´ ordova,Anomalies of (1 + 1)D categorical symmetries, [arXiv:2304.01262]

    work page arXiv

  57. [57]

    Cordova, P.-S

    C. Cordova, P.-S. Hsin, and C. Zhang, Anomalies of Non-Invertible Symmetries in (3+1)d , [arXiv:2308.11706]

    work page arXiv

  58. [58]

    Antinucci, F

    A. Antinucci, F. Benini, C. Copetti, G. Galati, and G. Rizi, Anomalies of non-invertible self-duality symmetries: fractionalization and gauging , [arXiv:2308.11707]

    work page arXiv

  59. [59]

    Bhardwaj, L

    L. Bhardwaj, L. E. Bottini, D. Pajer, and S. Schafer-Nameki, Gapped Phases with Non-Invertible Symmetries: (1+1)d , [arXiv:2310.03784]. 80

    work page arXiv

  60. [60]

    Bhardwaj, L

    L. Bhardwaj, L. E. Bottini, D. Pajer, and S. Schafer-Nameki, Categorical Landau Paradigm for Gapped Phases, [arXiv:2310.03786]

    work page arXiv

  61. [61]

    Choi, D.-C

    Y. Choi, D.-C. Lu, and Z. Sun, Self-duality under gauging a non-invertible symmetry , [arXiv:2310.19867]

    work page arXiv

  62. [62]

    Diatlyk, C

    O. Diatlyk, C. Luo, Y. Wang, and Q. Weller, Gauging Non-Invertible Symmetries: Topological Interfaces and Generalized Orbifold Groupoid in 2d QFT , [arXiv:2311.17044]

    work page arXiv

  63. [63]

    A. N. Schellekens and N. P. Warner, Conformal subalgebras of kac-moody algebras , Phys. Rev. D 34 (Nov, 1986) 3092–3096

    work page 1986

  64. [64]

    V. G. Ka and M. N. Sanielevici, Decompositions of representations of exceptional affine algebras with respect to conformal subalgebras , Phys. Rev. D 37 (Apr, 1988) 2231–2237

    work page 1988

  65. [65]

    Boysal and C

    A. Boysal and C. Pauly, Strange duality for verlinde spaces of exceptional groups at level one, International Mathematics Research Notices 2010 (2010), no. 4 595–618

    work page 2010

  66. [66]

    V. G. Kac, P. M. Frajria, P. Papi, and F. Xu, Conformal embeddings and simple current extensions, International Mathematics Research Notices 2015 (2015), no. 14 5229–5288

    work page 2015

  67. [67]

    Commutative Algebras in Fibonacci Categories

    A. Davydov and T. Booker, Commutative Algebras in Fibonacci Categories , [arXiv:1103.3537]

    work page internal anchor Pith review Pith/arXiv arXiv

  68. [68]

    V. A. Fateev and A. B. Zamolodchikov, Parafermionic Currents in the Two-Dimensional Conformal Quantum Field Theory and Selfdual Critical Points in Z(n) Invariant Statistical Systems, Sov. Phys. JETP 62 (1985) 215–225

    work page 1985

  69. [69]

    Mukhi and B

    S. Mukhi and B. C. Rayhaun, Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25 , Commun. Math. Phys. 401 (2023), no. 2 1899–1949, [arXiv:2208.05486]

    work page arXiv 2023

  70. [70]

    B. C. Rayhaun, Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality , [arXiv:2303.16921]

    work page arXiv

  71. [71]

    A. N. Schellekens, Meromorphic C = 24 conformal field theories , Commun. Math. Phys. 153 (1993) 159–186, [ hep-th/9205072]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  72. [72]

    Goddard, A

    P. Goddard, A. Kent, and D. I. Olive, Virasoro Algebras and Coset Space Models , Phys. Lett. B 152 (1985) 88–92

    work page 1985

  73. [73]

    Goddard, A

    P. Goddard, A. Kent, and D. I. Olive, Unitary Representations of the Virasoro and Supervirasoro Algebras, Commun. Math. Phys. 103 (1986) 105–119. 81

    work page 1986

  74. [74]

    The resolution of field identification fixed points in diagonal coset theories

    J. Fuchs, B. Schellekens, and C. Schweigert, The resolution of field identification fixed points in diagonal coset theories , Nucl. Phys. B 461 (1996) 371–406, [ hep-th/9509105]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  75. [75]

    Gepner, Field Identification in Coset Conformal Field Theories , Phys

    D. Gepner, Field Identification in Coset Conformal Field Theories , Phys. Lett. B 222 (1989) 207–212

    work page 1989

  76. [76]

    A. N. Schellekens and S. Yankielowicz, Field Identification Fixed Points in the Coset Construction, Nucl. Phys. B 334 (1990) 67–102

    work page 1990

  77. [77]

    Delmastro, J

    D. Delmastro, J. Gomis, and M. Yu, Infrared phases of 2d QCD , JHEP 02 (2023) 157, [arXiv:2108.02202]

    work page arXiv 2023

  78. [78]

    Komargodski, K

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

    work page arXiv 2021

  79. [79]

    Spiegelglas, Setting fusion rings in topological landau-ginzburg , Physics Letters B 274 (1992), no

    M. Spiegelglas, Setting fusion rings in topological landau-ginzburg , Physics Letters B 274 (1992), no. 1 21–26

    work page 1992

  80. [80]

    $G/G$--Topological Field Theories by Cosetting $G_k$

    M. Spiegelglas and S. Yankielowicz, G / G topological field theories by cosetting G(k) , Nucl. Phys. B 393 (1993) 301–336, [ hep-th/9201036]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

Showing first 80 references.