"Zoology'' of non-invertible duality defects: the view from class $\mathcal{S}$

We study generalizations of the non-invertible duality defects present in N = 4 SU(N) SYM by considering theories with larger duality groups. We focus on 4d N = 2 theories of class S obtained by the dimensional reduction of the 6d N = (2, 0) theory of AN−1 type on a Riemann surface Σg without punctures. We discuss their non-invertible duality symmetries and provide two ways to compute their fusion algebra: either using discrete topological manipulations or a 5d TQFT description. Finally, we introduce the concept of “rank” of a non-invertible duality symmetry and show how it can be used to (almost) completely fix the fusion algebra with little computational effort.

[1]  Yi-Nan Wang,et al.  Symmetry TFTs for 3d QFTs from M-theory , 2022, Journal of High Energy Physics.

[2]  Noppadol Mekareeya,et al.  Mixed anomalies, two-groups, non-invertible symmetries, and 3d superconformal indices , 2022, Journal of High Energy Physics.

[3]  Pierluigi Niro,et al.  Exploring non-invertible symmetries in free theories , 2022, Journal of High Energy Physics.

[4]  S. Schäfer-Nameki,et al.  Noninvertible Symmetries from Holography and Branes. , 2022, Physical review letters.

[5]  Ho Tat Lam,et al.  Noninvertible Time-Reversal Symmetry. , 2022, Physical review letters.

[6]  K. Ohmori,et al.  Noninvertible Chiral Symmetry and Exponential Hierarchies , 2022, Physical Review X.

[7]  A. Tiwari,et al.  Non-invertible higher-categorical symmetries , 2022, SciPost Physics.

[8]  F. Benini,et al.  Factorization and global symmetries in holography , 2022, SciPost Physics.

[9]  A. Tiwari,et al.  Non-Invertible Symmetry Webs , 2022, 2212.06842.

[10]  A. Tiwari,et al.  Unifying Constructions of Non-Invertible Symmetries , 2022, 2212.06159.

[11]  Ryo Yokokura.  Non-invertible symmetries in axion electrodynamics , 2022, 2212.05001.

[12]  Ho Tat Lam,et al.  Non-invertible Gauss Law and Axions , 2022, 2212.04499.

[13]  Iñaki García Etxebarria,et al.  A Goldstone theorem for continuous non-invertible symmetries , 2022, 2211.09570.

[14]  Sungwoo Hong,et al.  Neutrino Masses from Generalized Symmetry Breaking , 2022, 2211.07639.

[15]  Shih-Hsuan Chen,et al.  Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT , 2022, 2210.13780.

[16]  F. Benini,et al.  The holography of non-invertible self-duality symmetries , 2022, 2210.09146.

[17]  Yunqin Zheng,et al.  Symmetry TFTs for Non-Invertible Defects , 2022, 2209.11062.

[18]  J. Heckman,et al.  The Branes Behind Generalized Symmetry Operators , 2022, Fortschritte der Physik.

[19]  Iñaki García Etxebarria.  Branes and Non-Invertible Symmetries , 2022, 2208.07508.

[20]  S. Schäfer-Nameki,et al.  Universal Non‐Invertible Symmetries , 2022, Fortschritte der Physik.

[21]  Ling Lin,et al.  Decomposition, Condensation Defects, and Fusion , 2022, Fortschritte der Physik.

[22]  T. Bartsch,et al.  Non-invertible Symmetries and Higher Representation Theory II , 2022, 2208.05993.

[23]  R. Argurio,et al.  Non-invertible defects in 5d, boundaries and holography , 2022, SciPost Physics.

[24]  R. Argurio,et al.  Continuous Generalized Symmetries in Three Dimensions , 2022, 2206.14093.

[25]  M. Zotto,et al.  On the 6d Origin of Non-invertible Symmetries in 4d , 2022, 2206.07073.

[26]  Andrea Antinucci,et al.  On continuous 2-category symmetries and Yang-Mills theory , 2022, Journal of High Energy Physics.

[27]  Ho Tat Lam,et al.  Noninvertible Global Symmetries in the Standard Model. , 2022, Physical review letters.

[28]  Ho Tat Lam,et al.  Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions , 2022, 2204.09025.

[29]  D. Rodŕıguez-Gómez,et al.  Non-Invertible Symmetries from Discrete Gauging and Completeness of the Spectrum , 2022, 2204.07523.

[30]  Konstantinos Roumpedakis,et al.  Higher Gauging and Non-invertible Condensation Defects , 2022, 2204.02407.

[31]  Sakura Schafer-Nameki,et al.  Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S , 2021, SciPost Physics.

[32]  Yunqin Zheng,et al.  Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories. , 2021, Physical review letters.

[33]  Z. Komargodski,et al.  Higher central charges and topological boundaries in 2+1-dimensional TQFTs , 2021, SciPost Physics.

[34]  Saghar Hosseini,et al.  Symmetry TFTs from String Theory , 2021, Communications in Mathematical Physics.

[35]  Ryan Thorngren,et al.  Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond , 2021, 2106.12577.

[36]  Sakura Schafer-Nameki,et al.  1-form symmetries of 4d N=2 class S theories , 2021, SciPost Physics.

[37]  Yuji Tachikawa,et al.  SL(2, ℤ) action on QFTs with ℤ2 symmetry and the Brown-Kervaire invariants , 2020, Journal of High Energy Physics.

[38]  Z. Komargodski,et al.  Symmetries and strings of adjoint QCD2 , 2020, Journal of High Energy Physics.

[39]  Yifan Wang,et al.  Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases , 2019, 1912.02817.

[40]  Ho Tat Lam,et al.  Comments on one-form global symmetries and their gauging in 3d and 4d , 2018, SciPost Physics.

[41]  Y. Wang,et al.  Topological defect lines and renormalization group flows in two dimensions , 2018, Journal of High Energy Physics.

[42]  Samuel Monnier.  The anomaly field theories of six-dimensional (2,0) superconformal theories , 2017, 1706.01903.

[43]  Nathan Seiberg,et al.  Generalized global symmetries , 2014, 1412.5148.

[44]  A. Kapustin,et al.  Coupling a QFT to a TQFT and duality , 2014, 1401.0740.

[45]  Yuji Tachikawa.  On the 6d origin of discrete additional data of 4d gauge theories , 2013, 1309.0697.

[46]  O. Aharony,et al.  Reading between the lines of four-dimensional gauge theories , 2013, 1305.0318.

[47]  D. Gaiotto.  Preprint Typeset in Jhep Style -hyper Version N = 2 Dualities , 2022 .

[48]  G. Moore,et al.  Framed BPS states , 2010, 1006.0146.

[49]  E. Witten.  Geometric Langlands From Six Dimensions , 2009, 0905.2720.

[50]  J. Fuchs,et al.  DUALITY AND DEFECTS IN RATIONAL CONFORMAL FIELD THEORY , 2006, hep-th/0607247.

[51]  J. Fröhlich,et al.  Kramers-wannier duality from conformal defects. , 2004, Physical review letters.

[52]  J. Zuber,et al.  Generalised twisted partition functions , 2000, hep-th/0011021.

[53]  T. Breuer.  Characters and Automorphism Groups of Compact Riemann Surfaces , 2000 .

[54]  Clifford V. Johnson.  FROM M-THEORY TO F-THEORY, WITH BRANES , 1997, hep-th/9706155.

[55]  E. Verlinde,et al.  Fusion Rules and Modular Transformations in 2D Conformal Field Theory , 1988 .