Abstract
We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category Rep(H) of a semisimple weak Hopf algebra H, the fermionized TQFT has a superfusion category symmetry SRep(\( \mathcal{H} \)u), which is the supercategory of super representations of a weak Hopf superalgebra \( \mathcal{H} \)u. The weak Hopf superalgebra \( \mathcal{H} \)u depends not only on H but also on a choice of a non-anomalous ℤ2 subgroup of Rep(H) that is used for the fermionization. We derive a general formula for \( \mathcal{H} \)u by explicitly constructing fermionic TQFTs with SRep(\( \mathcal{H} \)u) symmetry. We also construct lattice Hamiltonians of fermionic gapped phases when the symmetry is non-anomalous. As concrete examples, we compute the fermionization of finite group symmetries, the symmetries of finite gauge theories, and duality symmetries. We find that the fermionization of duality symmetries depends crucially on F-symbols of the original fusion categories. The computation of the above concrete examples suggests that our fermionization formula of fusion category symmetries can also be applied to non-topological QFTs.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
C.L. Douglas and D.J. Reutter, Fusion 2-categories and a state-sum invariant for 4-manifolds, arXiv:1812.11933.
D. Gaiotto and T. Johnson-Freyd, Condensations in higher categories, arXiv:1905.09566 [INSPIRE].
T. Johnson-Freyd, On the Classification of Topological Orders, Commun. Math. Phys. 393 (2022) 989 [arXiv:2003.06663] [INSPIRE].
L. Kong et al., Classification of topological phases with finite internal symmetries in all dimensions, JHEP 09 (2020) 093 [arXiv:2003.08898] [INSPIRE].
L. Kong et al., Algebraic higher symmetry and categorical symmetry — a holographic and entanglement view of symmetry, Phys. Rev. Res. 2 (2020) 043086 [arXiv:2005.14178] [INSPIRE].
J. McGreevy, Generalized Symmetries in Condensed Matter, arXiv:2204.03045 [https://doi.org/10.1146/annurev-conmatphys-040721-021029] [INSPIRE].
C. Córdova, T.T. Dumitrescu, K. Intriligator and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond, in the proceedings of the Snowmass 2021, Seattle U.S.A., July 17–26 (2022) [arXiv:2205.09545] [INSPIRE].
R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases, arXiv:1912.02817 [INSPIRE].
L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions, JHEP 03 (2018) 189 [arXiv:1704.02330] [INSPIRE].
P. Etingof, S. Gelaki, D. Nikshych and V. Ostrik, Tensor Categories, American Mathematical Society (2015) [https://doi.org/10.1090/surv/205].
E.P. Verlinde, Fusion Rules and Modular Transformations in 2D Conformal Field Theory, Nucl. Phys. B 300 (1988) 360 [INSPIRE].
V.B. Petkova and J.B. Zuber, Generalized twisted partition functions, Phys. Lett. B 504 (2001) 157 [hep-th/0011021] [INSPIRE].
J. Fuchs, I. Runkel and C. Schweigert, TFT construction of RCFT correlators 1. Partition functions, Nucl. Phys. B 646 (2002) 353 [hep-th/0204148] [INSPIRE].
J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Kramers-Wannier duality from conformal defects, Phys. Rev. Lett. 93 (2004) 070601 [cond-mat/0404051] [INSPIRE].
J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Duality and defects in rational conformal field theory, Nucl. Phys. B 763 (2007) 354 [hep-th/0607247] [INSPIRE].
J. Fuchs, M.R. Gaberdiel, I. Runkel and C. Schweigert, Topological defects for the free boson CFT, J. Phys. A 40 (2007) 11403 [arXiv:0705.3129] [INSPIRE].
J. Fröhlich, J. Fuchs, I. Runkel and C. Schweigert, Defect lines, dualities, and generalised orbifolds, in the proceedings of the 16th International Congress on Mathematical Physics, Prague Czechia, August 3–8 (2009) [https://doi.org/10.1142/9789814304634_0056] [arXiv:0909.5013] [INSPIRE].
C.-M. Chang et al., Topological Defect Lines and Renormalization Group Flows in Two Dimensions, JHEP 01 (2019) 026 [arXiv:1802.04445] [INSPIRE].
C.-M. Chang and Y.-H. Lin, Lorentzian dynamics and factorization beyond rationality, JHEP 10 (2021) 125 [arXiv:2012.01429] [INSPIRE].
R. Thorngren and Y. Wang, Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond, arXiv:2106.12577 [INSPIRE].
D. Gaiotto and J. Kulp, Orbifold groupoids, JHEP 02 (2021) 132 [arXiv:2008.05960] [INSPIRE].
A. Davydov, L. Kong and I. Runkel, Field theories with defects and the centre functor, arXiv:1107.0495 [INSPIRE].
N. Carqueville and I. Runkel, Orbifold completion of defect bicategories, Quantum Topol. 7 (2016) 203 [arXiv:1210.6363] [INSPIRE].
I. Brunner, N. Carqueville and D. Plencner, Orbifolds and topological defects, Commun. Math. Phys. 332 (2014) 669 [arXiv:1307.3141] [INSPIRE].
I. Brunner, N. Carqueville and D. Plencner, A quick guide to defect orbifolds, Proc. Symp. Pure Math. 88 (2014) 231 [arXiv:1310.0062] [INSPIRE].
I. Brunner, N. Carqueville and D. Plencner, Discrete torsion defects, Commun. Math. Phys. 337 (2015) 429 [arXiv:1404.7497] [INSPIRE].
Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, Symmetries and strings of adjoint QCD2, JHEP 03 (2021) 103 [arXiv:2008.07567] [INSPIRE].
T.-C. Huang and Y.-H. Lin, Topological field theory with Haagerup symmetry, J. Math. Phys. 63 (2022) 042306 [arXiv:2102.05664] [INSPIRE].
K. Inamura, Topological field theories and symmetry protected topological phases with fusion category symmetries, JHEP 05 (2021) 204 [arXiv:2103.15588] [INSPIRE].
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] [INSPIRE].
K. Inamura, On lattice models of gapped phases with fusion category symmetries, JHEP 03 (2022) 036 [arXiv:2110.12882] [INSPIRE].
V.G. Turaev and O.Y. Viro, State sum invariants of 3 manifolds and quantum 6j-symbols, Topology 31 (1992) 865 [INSPIRE].
J.W. Barrett and B.W. Westbury, Invariants of piecewise linear three manifolds, Trans. Am. Math. Soc. 348 (1996) 3997 [hep-th/9311155] [INSPIRE].
D.S. Freed and C. Teleman, Topological dualities in the Ising model, Geom. Topol. 26 (2022) 1907 [arXiv:1806.00008] [INSPIRE].
D.S. Freed and C. Teleman, Gapped Boundary Theories in Three Dimensions, Commun. Math. Phys. 388 (2021) 845 [arXiv:2006.10200] [INSPIRE].
D. Freed, Finite symmetry in QFT, 22060026 (2022).
A. Feiguin et al., Interacting anyons in topological quantum liquids: The golden chain, Phys. Rev. Lett. 98 (2007) 160409 [cond-mat/0612341] [INSPIRE].
M. Buican and A. Gromov, Anyonic Chains, Topological Defects, and Conformal Field Theory, Commun. Math. Phys. 356 (2017) 1017 [arXiv:1701.02800] [INSPIRE].
D. Aasen, R.S.K. Mong and P. Fendley, Topological Defects on the Lattice I: The Ising model, J. Phys. A 49 (2016) 354001 [arXiv:1601.07185] [INSPIRE].
D. Aasen, P. Fendley and R.S.K. Mong, Topological Defects on the Lattice: Dualities and Degeneracies, arXiv:2008.08598 [INSPIRE].
M. Hauru et al., Topological conformal defects with tensor networks, Phys. Rev. B 94 (2016) 115125 [arXiv:1512.03846] [INSPIRE].
J. Garre-Rubio, L. Lootens and A. Molnár, Classifying phases protected by matrix product operator symmetries using matrix product states, Quantum 7 (2023) 927 [arXiv:2203.12563] [INSPIRE].
T.-C. Huang et al., Numerical Evidence for a Haagerup Conformal Field Theory, Phys. Rev. Lett. 128 (2022) 231603 [arXiv:2110.03008] [INSPIRE].
R. Vanhove et al., Critical Lattice Model for a Haagerup Conformal Field Theory, Phys. Rev. Lett. 128 (2022) 231602 [arXiv:2110.03532] [INSPIRE].
Y. Liu, Y. Zou and S. Ryu, Operator fusion from wave-function overlap: Universal finite-size corrections and application to the Haagerup model, Phys. Rev. B 107 (2023) 155124 [arXiv:2203.14992] [INSPIRE].
D. Aasen, E. Lake and K. Walker, Fermion condensation and super pivotal categories, J. Math. Phys. 60 (2019) 121901 [arXiv:1709.01941] [INSPIRE].
J. Brundan and A.P. Ellis, Monoidal Supercategories, Commun. Math. Phys. 351 (2017) 1045 [arXiv:1603.05928].
R. Usher, Fermionic 6j-symbols in superfusion categories, J. Algebra 503 (2018) 453 [arXiv:1606.03466] [INSPIRE].
Z.-C. Gu, Z. Wang and X.-G. Wen, Classification of two-dimensional fermionic and bosonic topological orders, Phys. Rev. B 91 (2015) 125149 [arXiv:1010.1517] [INSPIRE].
S. Novak and I. Runkel, Spin from defects in two-dimensional quantum field theory, J. Math. Phys. 61 (2020) 063510 [arXiv:1506.07547] [INSPIRE].
I. Runkel and G.M.T. Watts, Fermionic CFTs and classifying algebras, JHEP 06 (2020) 025 [arXiv:2001.05055] [INSPIRE].
J. Lou, C. Shen, C. Chen and L.-Y. Hung, A (dummy’s) guide to working with gapped boundaries via (fermion) condensation, JHEP 02 (2021) 171 [arXiv:2007.10562] [INSPIRE].
K. Kikuchi, Emergent SUSY in two dimensions, arXiv:2204.03247 [INSPIRE].
R. Thorngren, Anomalies and Bosonization, Commun. Math. Phys. 378 (2020) 1775 [arXiv:1810.04414] [INSPIRE].
W. Ji, S.-H. Shao and X.-G. Wen, Topological Transition on the Conformal Manifold, Phys. Rev. Res. 2 (2020) 033317 [arXiv:1909.01425] [INSPIRE].
Y.-H. Lin and S.-H. Shao, Duality Defect of the Monster CFT, J. Phys. A 54 (2021) 065201 [arXiv:1911.00042] [INSPIRE].
I.M. Burbano, J. Kulp and J. Neuser, Duality defects in E8, JHEP 10 (2022) 186 [arXiv:2112.14323] [INSPIRE].
I. Makabe and G.M.T. Watts, Defects in the Tri-critical Ising model, JHEP 09 (2017) 013 [arXiv:1703.09148] [INSPIRE].
P.B. Smith, Boundary States and Anomalous Symmetries of Fermionic Minimal Models, arXiv:2102.02203 [INSPIRE].
Y. Fukusumi, Y. Tachikawa and Y. Zheng, Fermionization and boundary states in 1+1 dimensions, SciPost Phys. 11 (2021) 082 [arXiv:2103.00746] [INSPIRE].
H. Ebisu and M. Watanabe, Fermionization of conformal boundary states, Phys. Rev. B 104 (2021) 195124 [arXiv:2103.01101] [INSPIRE].
D. Gaiotto and A. Kapustin, Spin TQFTs and fermionic phases of matter, Int. J. Mod. Phys. A 31 (2016) 1645044 [arXiv:1505.05856] [INSPIRE].
Y. Tachikawa, Lecture on anomalies and topological phases, (2019) [https://member.ipmu.jp/yuji.tachikawa/lectures/2019-top-anom/].
A. Karch, D. Tong and C. Turner, A Web of 2d Dualities: Z2 Gauge Fields and Arf Invariants, SciPost Phys. 7 (2019) 007 [arXiv:1902.05550] [INSPIRE].
C.-T. Hsieh, Y. Nakayama and Y. Tachikawa, Fermionic minimal models, Phys. Rev. Lett. 126 (2021) 195701 [arXiv:2002.12283] [INSPIRE].
J. Kulp, Two More Fermionic Minimal Models, JHEP 03 (2021) 124 [arXiv:2003.04278] [INSPIRE].
F. Gliozzi, J. Scherk and D.I. Olive, Supersymmetry, Supergravity Theories and the Dual Spinor Model, Nucl. Phys. B 122 (1977) 253 [INSPIRE].
A. Kapustin, A. Turzillo and M. You, Spin Topological Field Theory and Fermionic Matrix Product States, Phys. Rev. B 98 (2018) 125101 [arXiv:1610.10075] [INSPIRE].
M. Fukuma, S. Hosono and H. Kawai, Lattice topological field theory in two-dimensions, Commun. Math. Phys. 161 (1994) 157 [hep-th/9212154] [INSPIRE].
C. Bachas and P.M.S. Petropoulos, Topological models on the lattice and a remark on string theory cloning, Commun. Math. Phys. 152 (1993) 191 [hep-th/9205031] [INSPIRE].
N. Carqueville, I. Runkel and G. Schaumann, Orbifolds of n-dimensional defect TQFTs, Geom. Topol. 23 (2019) 781 [arXiv:1705.06085] [INSPIRE].
V. Ostrik, Module categories, weak Hopf algebras and modular invariants, Transform. Groups 8 (2003) 177 [math/0111139].
T. Hayashi, A canonical Tannaka duality for finite seimisimple tensor categories, math/9904073.
A. Kapustin, A. Turzillo and M. You, Topological Field Theory and Matrix Product States, Phys. Rev. B 96 (2017) 075125 [arXiv:1607.06766] [INSPIRE].
K. Shiozaki and S. Ryu, Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions, JHEP 04 (2017) 100 [arXiv:1607.06504] [INSPIRE].
D. Nikshych, On the Structure of Weak Hopf Algebras, Adv. Math. 170 (2002) 257 [math/0106010].
P. Vecsernyés, Larson–Sweedler theorem and the role of grouplike elements in weak Hopf algebras, J. Algebra 270 (2003) 471 [math/0111045].
S. Novak and I. Runkel, State sum construction of two-dimensional topological quantum field theories on spin surfaces, J. Knot Theor. Ramifications 24 (2015) 1550028 [arXiv:1402.2839] [INSPIRE].
A. Chatterjee and X.-G. Wen, Symmetry as a shadow of topological order and a derivation of topological holographic principle, Phys. Rev. B 107 (2023) 155136 [arXiv:2203.03596] [INSPIRE].
G.I. Kac and V.G. Paljutkin, Finite ring groups (Translation), Trans. Mosc. Math. Soc˙ 15 251 (1966) [http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mmo&paperid=170&option_lang=eng].
Z.-C. Gu and X.-G. Wen, Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory, Phys. Rev. B 90 (2014) 115141 [arXiv:1201.2648] [INSPIRE].
D. Tambara and S. Yamagami, Tensor Categories with Fusion Rules of Self-Duality for Finite Abelian Groups, J. Algebra 209 (1998) 692.
J. Fuchs, C. Schweigert and A. Valentino, Bicategories for boundary conditions and for surface defects in 3-d TFT, Commun. Math. Phys. 321 (2013) 543 [arXiv:1203.4568] [INSPIRE].
A. Kapustin and N. Saulina, Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory, arXiv:1012.0911 [INSPIRE].
N. Carqueville, C. Meusburger and G. Schaumann, 3-dimensional defect TQFTs and their tricategories, Adv. Math. 364 (2020) 107024 [arXiv:1603.01171] [INSPIRE].
N. Carqueville, I. Runkel and G. Schaumann, Line and surface defects in Reshetikhin–Turaev TQFT, Quantum Topol. 10 (2018) 399 [arXiv:1710.10214] [INSPIRE].
N. Carqueville, I. Runkel and G. Schaumann, Orbifolds of Reshetikhin-Turaev TQFTs, Theor. Appl. Categor. 35 (2020) 513 [arXiv:1809.01483] [INSPIRE].
C. Meusburger, State sum models with defects based on spherical fusion categories, Adv. Math. 429 (2023) 109177 [arXiv:2205.06874] [INSPIRE].
M. Nguyen, Y. Tanizaki and M. Ünsal, Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality, JHEP 03 (2021) 238 [arXiv:2101.02227] [INSPIRE].
M. Koide, Y. Nagoya and S. Yamaguchi, Non-invertible topological defects in 4-dimensional ℤ2 pure lattice gauge theory, PTEP 2022 (2022) 013B03 [arXiv:2109.05992] [INSPIRE].
Y. Choi et al., Noninvertible duality defects in 3+1 dimensions, Phys. Rev. D 105 (2022) 125016 [arXiv:2111.01139] [INSPIRE].
J. Kaidi, K. Ohmori and Y. Zheng, Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories, Phys. Rev. Lett. 128 (2022) 111601 [arXiv:2111.01141] [INSPIRE].
K. Roumpedakis, S. Seifnashri and S.-H. Shao, Higher Gauging and Non-invertible Condensation Defects, Commun. Math. Phys. 401 (2023) 3043 [arXiv:2204.02407] [INSPIRE].
L. Bhardwaj, L.E. Bottini, S. Schafer-Nameki and A. Tiwari, Non-invertible higher-categorical symmetries, SciPost Phys. 14 (2023) 007 [arXiv:2204.06564] [INSPIRE].
G. Arias-Tamargo and D. Rodríguez-Gómez, Non-invertible symmetries from discrete gauging and completeness of the spectrum, JHEP 04 (2023) 093 [arXiv:2204.07523] [INSPIRE].
Y. Hayashi and Y. Tanizaki, Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly, JHEP 08 (2022) 036 [arXiv:2204.07440] [INSPIRE].
Y. Choi et al., Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions, Commun. Math. Phys. 402 (2023) 489 [arXiv:2204.09025] [INSPIRE].
J. Kaidi, G. Zafrir and Y. Zheng, Non-invertible symmetries of \( \mathcal{N} \) = 4 SYM and twisted compactification, JHEP 08 (2022) 053 [arXiv:2205.01104] [INSPIRE].
Y. Choi, H.T. Lam and S.-H. Shao, Noninvertible Global Symmetries in the Standard Model, Phys. Rev. Lett. 129 (2022) 161601 [arXiv:2205.05086] [INSPIRE].
C. Córdova and K. Ohmori, Noninvertible Chiral Symmetry and Exponential Hierarchies, Phys. Rev. X 13 (2023) 011034 [arXiv:2205.06243] [INSPIRE].
A. Antinucci, G. Galati and G. Rizi, On continuous 2-category symmetries and Yang-Mills theory, JHEP 12 (2022) 061 [arXiv:2206.05646] [INSPIRE].
V. Bashmakov, M. Del Zotto and A. Hasan, On the 6d origin of non-invertible symmetries in 4d, JHEP 09 (2023) 161 [arXiv:2206.07073] [INSPIRE].
C.T.C. Wall, Graded Brauer Groups, J. Reine Angew. Math. 213 (1964) 187.
T. Józefiak, Semisimple superalgebras, in Algebra Some Current Trends, L.L. Avramov and K.B. Tchakerian eds., Springer Berlin Heidelberg (1988), p. 96–113 [https://doi.org/10.1007/bfb0082020].
J. Fuchs and C. Stigner, On Frobenius algebras in rigid monoidal categories, arXiv:0901.4886.
S. Montgomery, Hopf Algebras and Their Actions on Rings, American Mathematical Society (1993) [https://doi.org/10.1090/cbms/082].
D. Nikshych, Semisimple weak Hopf algebras, J. Algebra 275 (2004) 639 [math/0304098].
N. Andruskiewitsch and J.M. Mombelli, On module categories over finite-dimensional Hopf algebras, J. Algebra 314 (2007) 383 [math/0608781].
C.E. Watts, Intrinsic characterizations of some additive functors, Proceedings of the American Mathematical Society 11 (1960) 5.
S. Eilenberg, Abstract Description of some Basic Functors, Journal of the Indian Mathematical Society 24 (1960) 231.
N. Andruskiewitsch, P. Etingof and S. Gelaki, Triangular Hopf algebras with the Chevalley property, Michigan Math. J. 49 (2001) 277 [math/0008232].
G. Böhm, F. Nill and K. Szlachányi, Weak Hopf Algebras: I. Integral Theory and C∗-Structure, J. Algebra 221 (1999) 385 [math/9805116].
D. Nikshych, V. Turaev and L. Vainerman, Invariants of knots and 3-manifolds from quantum groupoids, Topology Appl. 127 (2003) 91 [math/0006078].
H. Henker, Module Categories over Quasi-Hopf Algebras and Weak Hopf Algebras and the Projectivity of Hopf Modules, Ph.D. thesis, Ludwig-Maximilians-Universität München, München, Germany (2011) [https://doi.org/10.5282/edoc.13148].
J.A. Álvarez, J.F. Vilaboa and R.G. Rodríguez, Weak Braided Hopf Algebras, Indiana Univ. Math. J. 57 (2008) 2423.
C. Pastro and R. Street, Weak Hopf monoids in braided monoidal categories, Alg. Numb. Theor. 3 (2009) 149 [arXiv:0801.4067].
S. Majid, Cross Products by Braided Groups and Bosonization, J. Algebra 163 (1994) 165.
N. Andruskiewitsch, I. Angiono and H. Yamane, On pointed Hopf superalgebras, arXiv:1009.5148.
D. Tambara, Representations of tensor categories with fusion rules of self-duality for abelian groups, Israel Journal of Mathematics 118 (2000) 29.
S. Ryu and S.-C. Zhang, Interacting topological phases and modular invariance, Phys. Rev. B 85 (2012) 245132 [arXiv:1202.4484] [INSPIRE].
C. Mével, Exemples et applications des groupoïdes quantiques finis, Ph.D. thesis, Université de Caen, Caen, France (2010) [https://tel.archives-ouvertes.fr/tel-00498884].
D. Delmastro, D. Gaiotto and J. Gomis, Global anomalies on the Hilbert space, JHEP 11 (2021) 142 [arXiv:2101.02218] [INSPIRE].
G.W. Moore and G. Segal, D-branes and K-theory in 2D topological field theory, hep-th/0609042 [INSPIRE].
D.J. Williamson and Z. Wang, Hamiltonian models for topological phases of matter in three spatial dimensions, Annals Phys. 377 (2017) 311 [arXiv:1606.07144] [INSPIRE].
A.L. Bullivant, Exactly Solvable Models for Topological Phases of Matter and Emergent Excitations, Ph.D. thesis, Univeristy of Leeds, U.K. (2018) [https://etheses.whiterose.ac.uk/24586/].
N. Bultinck, D.J. Williamson, J. Haegeman and F. Verstraete, Fermionic matrix product states and one-dimensional topological phases, Phys. Rev. B 95 (2017) 075108 [arXiv:1610.07849] [INSPIRE].
Acknowledgments
The author thanks Ryohei Kobayashi for discussions, and Ryohei Kobayashi and Yunqin Zheng for comments on the manuscript. The author also thanks anonymous referees for helpful suggestions on the manuscript. The author is supported by FoPM, WINGS Program, the University of Tokyo, and also by JSPS Research Fellowship for Young Scientists.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2206.13159
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Inamura, K. Fermionization of fusion category symmetries in 1+1 dimensions. J. High Energ. Phys. 2023, 101 (2023). https://doi.org/10.1007/JHEP10(2023)101
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2023)101