Abstract
We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent theory revealing a ’t Hooft anomaly in the space of coupling constants when suitable compact scalar background fields are activated. Furthermore, the gauging procedure also implies that our main example has infinitely many non-invertible global symmetries. These can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we comment on the holographic realization of both 2-group global symmetries and non-invertible symmetries discussed here by introducing a corresponding four-dimensional bulk description in terms of dynamical gauge fields.
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].
A. Kapustin and R. Thorngren, Higher symmetry and gapped phases of gauge theories, arXiv:1309.4721 [INSPIRE].
E. Sharpe, Notes on generalized global symmetries in QFT, Fortsch. Phys. 63 (2015) 659 [arXiv:1508.04770] [INSPIRE].
R. Thorngren and C. von Keyserlingk, Higher SPT’s and a generalization of anomaly in-flow, arXiv:1511.02929 [INSPIRE].
Y. Tachikawa, On gauging finite subgroups, SciPost Phys. 8 (2020) 015 [arXiv:1712.09542] [INSPIRE].
C. Córdova, T.T. Dumitrescu and K. Intriligator, Exploring 2-Group Global Symmetries, JHEP 02 (2019) 184 [arXiv:1802.04790] [INSPIRE].
C. Delcamp and A. Tiwari, From gauge to higher gauge models of topological phases, JHEP 10 (2018) 049 [arXiv:1802.10104] [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].
J.C. Baez and A.D. Lauda, Higher-Dimensional Algebra V: 2-Groups, math/0307200.
J. Baez and U. Schreiber, Higher gauge theory: 2-connections on 2-bundles, hep-th/0412325 [INSPIRE].
U. Schreiber and K. Waldorf, Connections on non-abelian Gerbes and their Holonomy, arXiv:0808.1923.
P.-S. Hsin and H.T. Lam, Discrete theta angles, symmetries and anomalies, SciPost Phys. 10 (2021) 032 [arXiv:2007.05915] [INSPIRE].
S. Gukov, P.-S. Hsin and D. Pei, Generalized global symmetries of T[M] theories. Part I, JHEP 04 (2021) 232 [arXiv:2010.15890] [INSPIRE].
C. Cordova, T.T. Dumitrescu and K. Intriligator, 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories, JHEP 04 (2021) 252 [arXiv:2009.00138] [INSPIRE].
M. Del Zotto and K. Ohmori, 2-Group Symmetries of 6D Little String Theories and T-Duality, Annales Henri Poincare 22 (2021) 2451 [arXiv:2009.03489] [INSPIRE].
F. Apruzzi, S. Schafer-Nameki, L. Bhardwaj and J. Oh, The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs, SciPost Phys. 13 (2022) 024 [arXiv:2105.08724] [INSPIRE].
Y. Lee, K. Ohmori and Y. Tachikawa, Matching higher symmetries across Intriligator-Seiberg duality, JHEP 10 (2021) 114 [arXiv:2108.05369] [INSPIRE].
F. Apruzzi, L. Bhardwaj, D.S.W. Gould and S. Schafer-Nameki, 2-Group symmetries and their classification in 6d, SciPost Phys. 12 (2022) 098 [arXiv:2110.14647] [INSPIRE].
L.V. Delacrétaz, D.M. Hofman and G. Mathys, Superfluids as Higher-form Anomalies, SciPost Phys. 8 (2020) 047 [arXiv:1908.06977] [INSPIRE].
N. Seiberg, Y. Tachikawa and K. Yonekura, Anomalies of Duality Groups and Extended Conformal Manifolds, PTEP 2018 (2018) 073B04 [arXiv:1803.07366] [INSPIRE].
C. Córdova, D.S. Freed, H.T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I, SciPost Phys. 8 (2020) 001 [arXiv:1905.09315] [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].
P.-S. Hsin, A. Kapustin and R. Thorngren, Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena, Phys. Rev. B 102 (2020) 245113 [arXiv:2004.10758] [INSPIRE].
A. Kapustin and L. Spodyneiko, Higher-dimensional generalizations of Berry curvature, Phys. Rev. B 101 (2020) 235130 [arXiv:2001.03454] [INSPIRE].
Y. Choi and K. Ohmori, Higher Berry phase of fermions and index theorem, JHEP 09 (2022) 022 [arXiv:2205.02188] [INSPIRE].
F. Benini, P.-S. Hsin and N. Seiberg, Comments on global symmetries, anomalies, and duality in (2 + 1)d, JHEP 04 (2017) 135 [arXiv:1702.07035] [INSPIRE].
P.B. Genolini and L. Tizzano, Comments on Global Symmetries and Anomalies of 5d SCFTs, arXiv:2201.02190 [INSPIRE].
L. Bhardwaj, M. Bullimore, A.E.V. Ferrari and S. Schafer-Nameki, Anomalies of Generalized Symmetries from Solitonic Defects, arXiv:2205.15330 [INSPIRE].
D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, Time Reversal, and Temperature, JHEP 05 (2017) 091 [arXiv:1703.00501] [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].
J. Frohlich, 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].
L. Bhardwaj and Y. Tachikawa, On finite symmetries and their gauging in two dimensions, JHEP 03 (2018) 189 [arXiv:1704.02330] [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].
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].
R. Thorngren and Y. Wang, Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond, arXiv:2106.12577 [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].
I.M. Burbano, J. Kulp and J. Neuser, Duality defects in E8, JHEP 10 (2022) 186 [arXiv:2112.14323] [INSPIRE].
Y. Choi et al., Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions, arXiv:2204.09025 [INSPIRE].
K. Roumpedakis, S. Seifnashri and S.-H. Shao, Higher Gauging and Non-invertible Condensation Defects, arXiv:2204.02407 [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].
G. Arias-Tamargo and D. Rodriguez-Gomez, Non-invertible symmetries from discrete gauging and completeness of the spectrum, JHEP 04 (2023) 093 [arXiv:2204.07523] [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].
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].
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, arXiv:2206.07073 [INSPIRE].
D.M. Hofman and N. Iqbal, Goldstone modes and photonization for higher form symmetries, SciPost Phys. 6 (2019) 006 [arXiv:1802.09512] [INSPIRE].
E. Lake, Higher-form symmetries and spontaneous symmetry breaking, arXiv:1802.07747 [INSPIRE].
T. Brauner, Field theories with higher-group symmetry from composite currents, JHEP 04 (2021) 045 [arXiv:2012.00051] [INSPIRE].
B. Heidenreich et al., Chern-Weil global symmetries and how quantum gravity avoids them, JHEP 11 (2021) 053 [arXiv:2012.00009] [INSPIRE].
E. Witten, Dyons of Charge eθ/2π, Phys. Lett. B 86 (1979) 283 [INSPIRE].
T.D. Brennan and C. Cordova, Axions, higher-groups, and emergent symmetry, JHEP 02 (2022) 145 [arXiv:2011.09600] [INSPIRE].
Y. Hidaka, M. Nitta and R. Yokokura, Higher-form symmetries and 3-group in axion electrodynamics, Phys. Lett. B 808 (2020) 135672 [arXiv:2006.12532] [INSPIRE].
Y. Hidaka, M. Nitta and R. Yokokura, Topological axion electrodynamics and 4-group symmetry, Phys. Lett. B 823 (2021) 136762 [arXiv:2107.08753] [INSPIRE].
P. Benetti Genolini and L. Tizzano, Instantons, symmetries and anomalies in five dimensions, JHEP 04 (2021) 188 [arXiv:2009.07873] [INSPIRE].
K. Ohmori and L. Tizzano, Anomaly matching across dimensions and supersymmetric Cardy formulae, JHEP 22 (2020) 027 [arXiv:2112.13445] [INSPIRE].
L. Di Pietro and Z. Komargodski, Cardy formulae for SUSY theories in d = 4 and d = 6, JHEP 12 (2014) 031 [arXiv:1407.6061] [INSPIRE].
A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality, JHEP 04 (2014) 001 [arXiv:1401.0740] [INSPIRE].
D.M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018) 005 [arXiv:1707.08577] [INSPIRE].
S. Grozdanov and N. Poovuttikul, Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma, JHEP 04 (2019) 141 [arXiv:1707.04182] [INSPIRE].
N. Iqbal and N. Poovuttikul, 2-group global symmetries, hydrodynamics and holography, arXiv:2010.00320 [INSPIRE].
N. Iqbal and K. Macfarlane, Higher-form symmetry breaking and holographic flavour, arXiv:2107.00373 [INSPIRE].
O. DeWolfe and K. Higginbotham, Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT , Phys. Rev. D 103 (2021) 026011 [arXiv:2010.06594] [INSPIRE].
Y. Lee and Y. Zheng, Remarks on compatibility between conformal symmetry and continuous higher-form symmetries, Phys. Rev. D 104 (2021) 085005 [arXiv:2108.00732] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-De Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].
T. Andrade and D. Marolf, AdS/CFT beyond the unitarity bound, JHEP 01 (2012) 049 [arXiv:1105.6337] [INSPIRE].
E. Witten, SL(2,Z) action on three-dimensional conformal field theories with Abelian symmetry, in the proceedings of the From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, (2005) p. 1173–1200 [hep-th/0307041] [INSPIRE].
E. Witten, AdS / CFT correspondence and topological field theory, JHEP 12 (1998) 012 [hep-th/9812012] [INSPIRE].
D. Marolf and S.F. Ross, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].
R. Argurio and A. Caddeo, Comments on holographic level/rank dualities, JHEP 08 (2022) 097 [arXiv:2205.06115] [INSPIRE].
A. Das, R. Gregory and N. Iqbal, Higher-form symmetries, anomalous magnetohydrodynamics, and holography, arXiv:2205.03619 [INSPIRE].
J. Aguilera Damia, R. Argurio and E. Garcia-Valdecasas, 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].
N. Seiberg, T. Senthil, C. Wang and E. Witten, A Duality Web in 2+1 Dimensions and Condensed Matter Physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
A.M. Polyakov, Fermi-Bose Transmutations Induced by Gauge Fields, Mod. Phys. Lett. A 3 (1988) 325 [INSPIRE].
O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].
A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
F. Wilczek, Magnetic Flux, Angular Momentum, and Statistics, Phys. Rev. Lett. 48 (1982) 1144 [INSPIRE].
J.K. Jain, Composite fermion approach for the fractional quantum Hall effect, Phys. Rev. Lett. 63 (1989) 199 [INSPIRE].
Acknowledgments
We thank Eduardo Garcia-Valdecasas for collaboration at the initial stages of this work. We also thank Pietro Benetti Genolini, Francesco Benini, Daniel Brennan, Christian Copetti and Pierluigi Niro for helpful discussions. LT is grateful for the hospitality of the King’s College and SISSA where part of this work has been completed. JAD and RA are respectively a Postdoctoral Researcher and a Research Director of the F.R.S.-FNRS (Belgium). LT has been partially supported by funds from the Solvay Family. This research is further supported by IISN-Belgium (convention 4.4503.15) and by the F.R.S.-FNRS under the “Excellence of Science” EOS be.h project n. 30820817.
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: 2206.14093
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
Damia, J.A., Argurio, R. & Tizzano, L. Continuous generalized symmetries in three dimensions. J. High Energ. Phys. 2023, 164 (2023). https://doi.org/10.1007/JHEP05(2023)164
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2023)164