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Anomalies and gauging of U(1) symmetries (2401.10165v4)

Published 18 Jan 2024 in hep-th

Abstract: We propose the Symmetry TFT for theories with a $U(1)$ symmetry in arbitrary dimension. The Symmetry TFT describes the structure of the symmetry, its anomalies, and the possible topological manipulations. It is constructed as a BF theory of gauge fields for groups $U(1)$ and $\mathbb{R}$, and contains a continuum of topological operators. We also propose an operation that produces the Symmetry TFT for the theory obtained by dynamically gauging the $U(1)$ symmetry. We discuss many examples. As an interesting outcome, we obtain the Symmetry TFT for the non-invertible $\mathbb{Q}/\mathbb{Z}$ chiral symmetry in four dimensions.

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References (36)
  1. J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37, 95 (1971).
  2. C. G. Callan, Jr. and J. A. Harvey, Anomalies and Fermion Zero Modes on Strings and Domain Walls, Nucl. Phys. B 250, 427 (1985).
  3. D. S. Freed, Anomalies and Invertible Field Theories, Proc. Symp. Pure Math. 88, 25 (2014), arXiv:1404.7224 [hep-th] .
  4. D. Gaiotto and J. Kulp, Orbifold groupoids, JHEP 02, 132, arXiv:2008.05960 [hep-th] .
  5. D. S. Freed, G. W. Moore, and C. Teleman, Topological symmetry in quantum field theory,   (2022), arXiv:2209.07471 [hep-th] .
  6. J. Kaidi, K. Ohmori, and Y. Zheng, Symmetry TFTs for Non-Invertible Defects,   (2022), arXiv:2209.11062 [hep-th] .
  7. C. Zhang and C. Córdova, Anomalies of (1+1)11(1{+}1)( 1 + 1 )D categorical symmetries,   (2023), arXiv:2304.01262 [cond-mat.str-el] .
  8. C. Cordova, P.-S. Hsin, and C. Zhang, Anomalies of Non-Invertible Symmetries in (3+1)d,   (2023), arXiv:2308.11706 [hep-th] .
  9. Y. Choi, H. T. Lam, and S.-H. Shao, Noninvertible Global Symmetries in the Standard Model, Phys. Rev. Lett. 129, 161601 (2022a), arXiv:2205.05086 [hep-th] .
  10. C. Cordova and K. Ohmori, Noninvertible Chiral Symmetry and Exponential Hierarchies, Phys. Rev. X 13, 011034 (2023), arXiv:2205.06243 [hep-th] .
  11. T. D. Brennan and Z. Sun, A SymTFT for Continuous Symmetries,   (2024), arXiv:2401.06128 [hep-th] .
  12. F. Apruzzi and F. Bedogna, to appear.
  13. J. M. Maldacena, G. W. Moore, and N. Seiberg, D-brane charges in five-brane backgrounds, JHEP 10, 005, arXiv:hep-th/0108152 .
  14. T. Banks and N. Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83, 084019 (2011), arXiv:1011.5120 [hep-th] .
  15. A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality, JHEP 04, 001, arXiv:1401.0740 [hep-th] .
  16. The theory might contain other topological operators, for instance condensates [45] or theta-defects [46].
  17. F. Benini, C. Copetti, and L. Di Pietro, Factorization and global symmetries in holography, SciPost Phys. 14, 019 (2023), arXiv:2203.09537 [hep-th] .
  18. Y. Tachikawa, On gauging finite subgroups, SciPost Phys. 8, 015 (2020), arXiv:1712.09542 [hep-th] .
  19. R. Dijkgraaf and E. Witten, Topological Gauge Theories and Group Cohomology, Commun. Math. Phys. 129, 393 (1990).
  20. N. Seiberg and E. Witten, Gapped boundary phases of topological insulators via weak coupling, PTEP 2016, 12C101 (2016), arXiv:1602.04251 [cond-mat.str-el] .
  21. R. Thorngren and Y. Wang, Anomalous symmetries end at the boundary, JHEP 09, 017, arXiv:2012.15861 [hep-th] .
  22. C. Córdova and T. T. Dumitrescu, Candidate Phases for S⁢U⁢(2)𝑆𝑈2SU(2)italic_S italic_U ( 2 ) Adjoint QCD44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT with Two Flavors from 𝒩=2𝒩2\mathcal{N}{=}2caligraphic_N = 2 Supersymmetric Yang-Mills Theory,   (2018), arXiv:1806.09592 [hep-th] .
  23. C.-T. Hsieh, Discrete gauge anomalies revisited,   (2018), arXiv:1808.02881 [hep-th] .
  24. J. Davighi and N. Lohitsiri, The algebra of anomaly interplay, SciPost Phys. 10, 074 (2021), arXiv:2011.10102 [hep-th] .
  25. D. Tong, Lectures on the Quantum Hall Effect (2016) arXiv:1606.06687 [hep-th] .
  26. The boundary theory also inherits the topological surfaces U(0,m)⁢[γ3]subscript𝑈0𝑚delimited-[]subscript𝛾3U_{(0,m)}[\gamma_{3}]italic_U start_POSTSUBSCRIPT ( 0 , italic_m ) end_POSTSUBSCRIPT [ italic_γ start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ] which are theta-defects [46] constructed out of the lines Wn⁢[γ1]subscript𝑊𝑛delimited-[]subscript𝛾1W_{n}[\gamma_{1}]italic_W start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT [ italic_γ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ].
  27. A. Kapustin and R. Thorngren, Higher symmetry and gapped phases of gauge theories,   (2013), arXiv:1309.4721 [hep-th] .
  28. C. Córdova, T. T. Dumitrescu, and K. Intriligator, Exploring 2-group global symmetries, JHEP 02, 184, arXiv:1802.04790 [hep-th] .
  29. F. Benini, C. Córdova, and P.-S. Hsin, On 2-Group Global Symmetries and their Anomalies, JHEP 03, 118, arXiv:1803.09336 [hep-th] .
  30. The minimal mixed U⁢(1)𝑈1U(1)italic_U ( 1 ) Chern-Simons terms that are well defined are 14⁢π2⁢A⁢d⁢B⁢d⁢B14superscript𝜋2𝐴𝑑𝐵𝑑𝐵\frac{1}{4\pi^{2}}A\,dB\,dBdivide start_ARG 1 end_ARG start_ARG 4 italic_π start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG italic_A italic_d italic_B italic_d italic_B or 18⁢π2⁢(A⁢d⁢B⁢d⁢B+B⁢d⁢A⁢d⁢A)18superscript𝜋2𝐴𝑑𝐵𝑑𝐵𝐵𝑑𝐴𝑑𝐴\frac{1}{8\pi^{2}}(A\,dB\,dB+B\,dA\,dA)divide start_ARG 1 end_ARG start_ARG 8 italic_π start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG ( italic_A italic_d italic_B italic_d italic_B + italic_B italic_d italic_A italic_d italic_A ).
  31. For α=1/2𝛼12\alpha=1/2italic_α = 1 / 2 we can simply use the U⁢(1)1𝑈subscript11U(1)_{1}italic_U ( 1 ) start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT trivial spin-Chern-Simons theory. Indeed this is the only value that corresponds to an invertible symmetry, namely (−1)Fsuperscript1𝐹(-1)^{F}( - 1 ) start_POSTSUPERSCRIPT italic_F end_POSTSUPERSCRIPT.
  32. 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, 039 (2019), arXiv:1812.04716 [hep-th] .
  33. Y. Choi, H. T. Lam, and S.-H. Shao, Non-invertible Gauss Law and Axions,   (2022b), arXiv:2212.04499 [hep-th] .
  34. G. T. Horowitz, Exactly Soluble Diffeomorphism Invariant Theories, Commun. Math. Phys. 125, 417 (1989).
  35. K. Roumpedakis, S. Seifnashri, and S.-H. Shao, Higher Gauging and Non-invertible Condensation Defects, Commun. Math. Phys. 401, 3043 (2023), arXiv:2204.02407 [hep-th] .
  36. L. Bhardwaj, S. Schafer-Nameki, and A. Tiwari, Unifying constructions of non-invertible symmetries, SciPost Phys. 15, 122 (2023), arXiv:2212.06159 [hep-th] .
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