Abstract
We explore novel examples of RG flows preserving a non-invertible self-duality symmetry. Our main focus is on \( \mathcal{N} \) = 1 quadratic superpotential deformations of 4d \( \mathcal{N} \) = 4 super-Yang-Mills theory with gauge algebra \( \mathfrak{su}(N) \). A theory that can be obtained in this way is the so-called \( \mathcal{N} \) = 1* SYM where all adjoint chiral multiplets have a mass. Such IR theory exhibits a rich structure of vacua which we thoroughly examine. Our analysis elucidates the physics of spontaneous breaking of self-duality symmetry occurring in the degenerate gapped vacua. The construction can be generalized, taking as UV starting point a theory of class \( \mathcal{S} \), to demonstrate how non-invertible self-duality symmetries exist in a variety of \( \mathcal{N} \) = 1 SCFTs. We finally apply this understanding to prove that the conifold theory has a non-invertible self-duality symmetry.
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D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
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].
E. Witten, Quantum Field Theory and the Jones Polynomial, Commun. Math. Phys. 121 (1989) 351 [INSPIRE].
M. Barkeshli, P. Bonderson, M. Cheng and Z. Wang, Symmetry Fractionalization, Defects, and Gauging of Topological Phases, Phys. Rev. B 100 (2019) 115147 [arXiv:1410.4540] [INSPIRE].
C.-M. Chang et al., Topological Defect Lines and Renormalization Group Flows in Two Dimensions, JHEP 01 (2019) 026 [arXiv:1802.04445] [INSPIRE].
R. Thorngren and Y. Wang, Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases, arXiv:1912.02817 [INSPIRE].
D. Gaiotto and J. Kulp, Orbifold groupoids, JHEP 02 (2021) 132 [arXiv:2008.05960] [INSPIRE].
Z. Komargodski, K. Ohmori, K. Roumpedakis and S. Seifnashri, Symmetries and strings of adjoint QCD2, JHEP 03 (2021) 103 [arXiv:2008.07567] [INSPIRE].
R. Thorngren and Y. Wang, Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond, arXiv:2106.12577 [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].
I.M. Burbano, J. Kulp and J. Neuser, Duality defects in E8, JHEP 10 (2022) 186 [arXiv:2112.14323] [INSPIRE].
Y.-H. Lin and S.-H. Shao, Bootstrapping noninvertible symmetries, Phys. Rev. D 107 (2023) 125025 [arXiv:2302.13900] [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].
F. Apruzzi et al., Symmetry TFTs from String Theory, Commun. Math. Phys. 402 (2023) 895 [arXiv:2112.02092] [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].
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. Cordova 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].
J.A. Damia, R. Argurio and L. Tizzano, Continuous Generalized Symmetries in Three Dimensions, JHEP 23 (2023) 164 [arXiv:2206.14093] [INSPIRE].
J.A. Damia, R. Argurio and E. Garcia-Valdecasas, Non-invertible defects in 5d, boundaries and holography, SciPost Phys. 14 (2023) 067 [arXiv:2207.02831] [INSPIRE].
L. Bhardwaj, S. Schafer-Nameki and J. Wu, Universal Non-Invertible Symmetries, Fortsch. Phys. 70 (2022) 2200143 [arXiv:2208.05973] [INSPIRE].
T. Bartsch, M. Bullimore, A.E.V. Ferrari and J. Pearson, Non-invertible Symmetries and Higher Representation Theory I, arXiv:2208.05993 [INSPIRE].
F. Apruzzi, I. Bah, F. Bonetti and S. Schafer-Nameki, Noninvertible Symmetries from Holography and Branes, Phys. Rev. Lett. 130 (2023) 121601 [arXiv:2208.07373] [INSPIRE].
N. Mekareeya and M. Sacchi, Mixed anomalies, two-groups, non-invertible symmetries, and 3d superconformal indices, JHEP 01 (2023) 115 [arXiv:2210.02466] [INSPIRE].
S. Chen and Y. Tanizaki, Solitonic Symmetry beyond Homotopy: Invertibility from Bordism and Noninvertibility from Topological Quantum Field Theory, Phys. Rev. Lett. 131 (2023) 011602 [arXiv:2210.13780] [INSPIRE].
Y. Choi, H.T. Lam and S.-H. Shao, Non-invertible Gauss law and axions, JHEP 09 (2023) 067 [arXiv:2212.04499] [INSPIRE].
R. Yokokura, Non-invertible symmetries in axion electrodynamics, arXiv:2212.05001 [INSPIRE].
L. Bhardwaj, S. Schafer-Nameki and A. Tiwari, Unifying constructions of non-invertible symmetries, SciPost Phys. 15 (2023) 122 [arXiv:2212.06159] [INSPIRE].
L. Bhardwaj, L.E. Bottini, S. Schafer-Nameki and A. Tiwari, Non-invertible symmetry webs, SciPost Phys. 15 (2023) 160 [arXiv:2212.06842] [INSPIRE].
T. Bartsch, M. Bullimore, A.E.V. Ferrari and J. Pearson, Non-invertible Symmetries and Higher Representation Theory II, arXiv:2212.07393 [INSPIRE].
J.J. Heckman et al., Top down approach to topological duality defects, Phys. Rev. D 108 (2023) 046015 [arXiv:2212.09743] [INSPIRE].
C. Montonen and D.I. Olive, Magnetic Monopoles as Gauge Particles?, Phys. Lett. B 72 (1977) 117 [INSPIRE].
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [arXiv:1305.0318] [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].
K.A. Intriligator, Bonus symmetries of N = 4 superYang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].
A. Kapustin and E. Witten, Electric-Magnetic Duality And The Geometric Langlands Program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
P.C. Argyres, K.A. Intriligator, R.G. Leigh and M.J. Strassler, On inherited duality in N = 1d = 4 supersymmetric gauge theories, JHEP 04 (2000) 029 [hep-th/9910250] [INSPIRE].
I. García-Etxebarria and D. Regalado, \( \mathcal{N} \) = 3 four dimensional field theories, JHEP 03 (2016) 083 [arXiv:1512.06434] [INSPIRE].
O. Aharony, Y. Tachikawa and K. Gomi, S-folds and 4d N = 3 superconformal field theories, JHEP 06 (2016) 044 [arXiv:1602.08638] [INSPIRE].
P.C. Argyres and M. Martone, 4d \( \mathcal{N} \) = 2 theories with disconnected gauge groups, JHEP 03 (2017) 145 [arXiv:1611.08602] [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
N. Dorey, An elliptic superpotential for softly broken N = 4 supersymmetric Yang-Mills theory, JHEP 07 (1999) 021 [hep-th/9906011] [INSPIRE].
N. Dorey and S.P. Kumar, Softly broken N = 4 supersymmetry in the large N limit, JHEP 02 (2000) 006 [hep-th/0001103] [INSPIRE].
N. Dorey, T.J. Hollowood and S.P. Kumar, An exact elliptic superpotential for N = 1* deformations of finite N = 2 gauge theories, Nucl. Phys. B 624 (2002) 95 [hep-th/0108221] [INSPIRE].
C.-T. Hsieh, Y. Tachikawa and K. Yonekura, Anomaly of the Electromagnetic Duality of Maxwell Theory, Phys. Rev. Lett. 123 (2019) 161601 [arXiv:1905.08943] [INSPIRE].
C.-T. Hsieh, Y. Tachikawa and K. Yonekura, Anomaly Inflow and p-Form Gauge Theories, Commun. Math. Phys. 391 (2022) 495 [arXiv:2003.11550] [INSPIRE].
A. Debray, M. Dierigl, J.J. Heckman and M. Montero, The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland, arXiv:2302.00007 [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].
V. Bashmakov, M. Del Zotto, A. Hasan and J. Kaidi, Non-invertible symmetries of class S theories, JHEP 05 (2023) 225 [arXiv:2211.05138] [INSPIRE].
A. Antinucci, C. Copetti, G. Galati and G. Rizi, ”Zoology” of non-invertible duality defects: the view from class \( \mathcal{S} \), arXiv:2212.09549 [INSPIRE].
F. Carta, S. Giacomelli, N. Mekareeya and A. Mininno, Comments on Non-invertible Symmetries in Argyres-Douglas Theories, JHEP 07 (2023) 135 [arXiv:2303.16216] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
M. Del Zotto, J.J. Heckman, D.S. Park and T. Rudelius, On the Defect Group of a 6D SCFT, Lett. Math. Phys. 106 (2016) 765 [arXiv:1503.04806] [INSPIRE].
L. Bhardwaj, M. Hubner and S. Schafer-Nameki, 1-form Symmetries of 4d N = 2 Class S Theories, SciPost Phys. 11 (2021) 096 [arXiv:2102.01693] [INSPIRE].
L. Bhardwaj, S. Giacomelli, M. Hübner and S. Schäfer-Nameki, Relative defects in relative theories: Trapped higher-form symmetries and irregular punctures in class S, SciPost Phys. 13 (2022) 101 [arXiv:2201.00018] [INSPIRE].
E. Witten, Dyons of Charge eθ/2π, Phys. Lett. B 86 (1979) 283 [INSPIRE].
O. Bergman and S. Hirano, The holography of duality in \( \mathcal{N} \) = 4 Super-Yang-Mills theory, JHEP 11 (2022) 069 [arXiv:2208.09396] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II, SciPost Phys. 8 (2020) 002 [arXiv:1905.13361] [INSPIRE].
J.P. Ang, K. Roumpedakis and S. Seifnashri, Line Operators of Gauge Theories on Non-Spin Manifolds, JHEP 04 (2020) 087 [arXiv:1911.00589] [INSPIRE].
L. Bhardwaj, Y. Lee and Y. Tachikawa, SL(2, ℤ) action on QFTs with ℤ2 symmetry and the Brown-Kervaire invariants, JHEP 11 (2020) 141 [arXiv:2009.10099] [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].
C. Beem, L. Rastelli, A. Sen and B.C. van Rees, Resummation and S-duality in N = 4 SYM, JHEP 04 (2014) 122 [arXiv:1306.3228] [INSPIRE].
J. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136 [INSPIRE].
J. Kaidi, K. Ohmori and Y. Zheng, Symmetry TFTs for Non-invertible Defects, Commun. Math. Phys. 404 (2023) 1021 [arXiv:2209.11062] [INSPIRE].
A. Antinucci et al., The holography of non-invertible self-duality symmetries, arXiv:2210.09146 [INSPIRE].
A. Apte, C. Cordova and H.T. Lam, Obstructions to gapped phases from noninvertible symmetries, Phys. Rev. B 108 (2023) 045134 [arXiv:2212.14605] [INSPIRE].
A. Antinucci et al., Anomalies of non-invertible self-duality symmetries: fractionalization and gauging, arXiv:2308.11707 [INSPIRE].
F. Benini, C. Córdova and P.-S. Hsin, On 2-Group Global Symmetries and their Anomalies, JHEP 03 (2019) 118 [arXiv:1803.09336] [INSPIRE].
Y. Tachikawa, On gauging finite subgroups, SciPost Phys. 8 (2020) 015 [arXiv:1712.09542] [INSPIRE].
P. Niro, K. Roumpedakis and O. Sela, Exploring non-invertible symmetries in free theories, JHEP 03 (2023) 005 [arXiv:2209.11166] [INSPIRE].
J. Kaidi, E. Nardoni, G. Zafrir and Y. Zheng, Symmetry TFTs and anomalies of non-invertible symmetries, JHEP 10 (2023) 053 [arXiv:2301.07112] [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
N. Halmagyi, C. Romelsberger and N.P. Warner, Inherited duality and quiver gauge theory, Adv. Theor. Math. Phys. 10 (2006) 159 [hep-th/0406143] [INSPIRE].
D.-E. Diaconescu, M.R. Douglas and J. Gomis, Fractional branes and wrapped branes, JHEP 02 (1998) 013 [hep-th/9712230] [INSPIRE].
M. Bertolini et al., Fractional D-branes and their gauge duals, JHEP 02 (2001) 014 [hep-th/0011077] [INSPIRE].
J. Polchinski, N = 2 Gauge/gravity duals, Int. J. Mod. Phys. A 16 (2001) 707 [hep-th/0011193] [INSPIRE].
I.R. Klebanov and N.A. Nekrasov, Gravity duals of fractional branes and logarithmic RG flow, Nucl. Phys. B 574 (2000) 263 [hep-th/9911096] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Gravity duals of supersymmetric SU(N) × SU(N + M) gauge theories, Nucl. Phys. B 578 (2000) 123 [hep-th/0002159] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χSB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
M.J. Strassler, The Duality cascade, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2003): Recent Trends in String Theory, Boulder, U.S.A., June 01–27 (2003), p. 419–510 [https://doi.org/10.1142/9789812775108_0005] [hep-th/0505153] [INSPIRE].
K.A. Intriligator and N. Seiberg, Duality, monopoles, dyons, confinement and oblique confinement in supersymmetric SO(Nc) gauge theories, Nucl. Phys. B 444 (1995) 125 [hep-th/9503179] [INSPIRE].
B.S. Acharya and C. Vafa, On domain walls of N = 1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011 [INSPIRE].
O. Aharony, N. Dorey and S.P. Kumar, New modular invariance in the N = 1* theory, operator mixings and supergravity singularities, JHEP 06 (2000) 026 [hep-th/0006008] [INSPIRE].
Acknowledgments
We thank Ofer Aharony, Michele Del Zotto, Ho Tat Lam, Kantaro Ohmori, and Yifan Wang for helpful discussions. J.A.D. and R.A. are respectively a Postdoctoral Researcher and a Research Director of the F.R.S.-FNRS (Belgium). The research of J.A.D., R.A. and L.T. is supported by IISN-Belgium (convention 4.4503.15) and through an ARC advanced project. F.B. and C.C. are supported by the ERC-COG grant NP-QFT No. 864583 “Nonperturbative dynamics of quantum fields: from new deconfined phases of matter to quantum black holes”, by the MUR-FARE grant EmGrav No. R20E8NR3HX “The Emergence of Quantum Gravity from Strong Coupling Dynamics”, and by the INFN “Iniziativa Specifica ST&FI”. S.B. is partially supported by the INFN “Iniziativa Specifica GAST”. L.T. has been partially supported by funds from the Solvay Family.
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Damia, J.A., Argurio, R., Benini, F. et al. Non-invertible symmetries along 4d RG flows. J. High Energ. Phys. 2024, 84 (2024). https://doi.org/10.1007/JHEP02(2024)084
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DOI: https://doi.org/10.1007/JHEP02(2024)084