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Non-invertible Symmetries in 2D from Type IIB String Theory (2310.15339v2)

Published 23 Oct 2023 in hep-th

Abstract: We propose a top-down approach to non-invertible symmetries in 2D QFTs and their associated symmetry topological field theories. We focus on the gauge theory engineered on D1-branes probing a particular Calabi-Yau 4-fold singularity. We show how to derive the symmetry topological field theory, a 3D Dijkgraaf-Witten theory, from the IIB supergravity under dimensional reduction. We also identify branes behind the non-invertible topological lines by dimensionally reducing their worldvolume actions. The action of non-invertible lines on charged local operators is then realized as the Hanany-Witten transition.

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References (83)
  1. D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP 02 (2015) 172, arXiv:1412.5148 [hep-th].
  2. C. Cordova, T. T. Dumitrescu, K. Intriligator, and S.-H. Shao, “Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond,” in 2022 Snowmass Summer Study. 5, 2022. arXiv:2205.09545 [hep-th].
  3. S. Schafer-Nameki, “ICTP Lectures on (Non-)Invertible Generalized Symmetries,” arXiv:2305.18296 [hep-th].
  4. L. Bhardwaj, L. E. Bottini, L. Fraser-Taliente, L. Gladden, D. S. W. Gould, A. Platschorre, and H. Tillim, “Lectures on Generalized Symmetries,” arXiv:2307.07547 [hep-th].
  5. R. Luo, Q.-R. Wang, and Y.-N. Wang, “Lecture Notes on Generalized Symmetries and Applications,” 7, 2023. arXiv:2307.09215 [hep-th].
  6. S.-H. Shao, “What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetry,” arXiv:2308.00747 [hep-th].
  7. M. Del Zotto, J. J. Heckman, D. S. Park, and T. Rudelius, “On the Defect Group of a 6D SCFT,” Lett. Math. Phys. 106 no. 6, (2016) 765–786, arXiv:1503.04806 [hep-th].
  8. I. Garcia Etxebarria, B. Heidenreich, and D. Regalado, “IIB flux non-commutativity and the global structure of field theories,” JHEP 10 (2019) 169, arXiv:1908.08027 [hep-th].
  9. F. Albertini, M. Del Zotto, I. García Etxebarria, and S. S. Hosseini, “Higher Form Symmetries and M-theory,” JHEP 12 (2020) 203, arXiv:2005.12831 [hep-th].
  10. D. R. Morrison, S. Schafer-Nameki, and B. Willett, “Higher-Form Symmetries in 5d,” JHEP 09 (2020) 024, arXiv:2005.12296 [hep-th].
  11. F. Apruzzi, I. Bah, F. Bonetti, and S. Schafer-Nameki, “Noninvertible Symmetries from Holography and Branes,” Phys. Rev. Lett. 130 no. 12, (2023) 121601, arXiv:2208.07373 [hep-th].
  12. I. Garcia Etxebarria, “Branes and Non-Invertible Symmetries,” Fortsch. Phys. 70 no. 11, (2022) 2200154, arXiv:2208.07508 [hep-th].
  13. J. J. Heckman, M. Hübner, E. Torres, and H. Y. Zhang, “The Branes Behind Generalized Symmetry Operators,” arXiv:2209.03343 [hep-th].
  14. J. J. Heckman, M. Hubner, E. Torres, X. Yu, and H. Y. Zhang, “Top down approach to topological duality defects,” Phys. Rev. D 108 no. 4, (2023) 046015, arXiv:2212.09743 [hep-th].
  15. F. Apruzzi, F. Bonetti, D. S. W. Gould, and S. Schafer-Nameki, “Aspects of Categorical Symmetries from Branes: SymTFTs and Generalized Charges,” arXiv:2306.16405 [hep-th].
  16. I. Bah, E. Leung, and T. Waddleton, “Non-Invertible Symmetries, Brane Dynamics, and Tachyon Condensation,” arXiv:2306.15783 [hep-th].
  17. M. Dierigl, J. J. Heckman, M. Montero, and E. Torres, “R7-Branes as Charge Conjugation Operators,” arXiv:2305.05689 [hep-th].
  18. M. Cvetič, J. J. Heckman, M. Hübner, and E. Torres, “Fluxbranes, Generalized Symmetries, and Verlinde’s Metastable Monopole,” arXiv:2305.09665 [hep-th].
  19. C. Lawrie, X. Yu, and H. Y. Zhang, “Intermediate Defect Groups, Polarization Pairs, and Non-invertible Duality Defects,” arXiv:2306.11783 [hep-th].
  20. E. P. Verlinde, “Fusion Rules and Modular Transformations in 2D Conformal Field Theory,” Nucl. Phys. B 300 (1988) 360–376.
  21. J. Fuchs, I. Runkel, and C. Schweigert, “TFT construction of RCFT correlators 1. Partition functions,” Nucl. Phys. B 646 (2002) 353–497, arXiv:hep-th/0204148.
  22. J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, “Kramers-Wannier duality from conformal defects,” Phys. Rev. Lett. 93 (2004) 070601, arXiv:cond-mat/0404051.
  23. L. Bhardwaj and Y. Tachikawa, “On finite symmetries and their gauging in two dimensions,” JHEP 03 (2018) 189, arXiv:1704.02330 [hep-th].
  24. C.-M. Chang, Y.-H. Lin, S.-H. Shao, Y. Wang, and X. Yin, “Topological Defect Lines and Renormalization Group Flows in Two Dimensions,” JHEP 01 (2019) 026, arXiv:1802.04445 [hep-th].
  25. R. Thorngren and Y. Wang, “Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases,” arXiv:1912.02817 [hep-th].
  26. Z. Komargodski, K. Ohmori, K. Roumpedakis, and S. Seifnashri, “Symmetries and strings of adjoint QCD22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT,” JHEP 03 (2021) 103, arXiv:2008.07567 [hep-th].
  27. R. Thorngren and Y. Wang, “Fusion Category Symmetry II: Categoriosities at c𝑐citalic_c = 1 and Beyond,” arXiv:2106.12577 [hep-th].
  28. S. Franco, D. Ghim, S. Lee, R.-K. Seong, and D. Yokoyama, “2d (0,2) Quiver Gauge Theories and D-Branes,” JHEP 09 (2015) 072, arXiv:1506.03818 [hep-th].
  29. S. Franco, S. Lee, and R.-K. Seong, “Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers,” JHEP 02 (2016) 047, arXiv:1510.01744 [hep-th].
  30. S. Franco, S. Lee, and R.-K. Seong, “Brane brick models and 2d (0, 2) triality,” JHEP 05 (2016) 020, arXiv:1602.01834 [hep-th].
  31. S. Franco, S. Lee, R.-K. Seong, and C. Vafa, “Brane Brick Models in the Mirror,” JHEP 02 (2017) 106, arXiv:1609.01723 [hep-th].
  32. S. Franco, S. Lee, and R.-K. Seong, “Orbifold Reduction and 2d (0,2) Gauge Theories,” JHEP 03 (2017) 016, arXiv:1609.07144 [hep-th].
  33. S. Franco, D. Ghim, S. Lee, and R.-K. Seong, “Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models,” JHEP 06 (2017) 068, arXiv:1702.02948 [hep-th].
  34. S. Franco and G. Musiker, “Higher Cluster Categories and QFT Dualities,” Phys. Rev. D 98 no. 4, (2018) 046021, arXiv:1711.01270 [hep-th].
  35. S. Franco and A. Hasan, “3⁢d3𝑑3d3 italic_d printing of 2⁢d2𝑑2d2 italic_d 𝒩=(0,2)𝒩02\mathcal{N}=\left(0,2\right)caligraphic_N = ( 0 , 2 ) gauge theories,” JHEP 05 (2018) 082, arXiv:1801.00799 [hep-th].
  36. S. Franco, A. Hasan, and X. Yu, “On the Classification of Duality Webs for Graded Quivers,” JHEP 06 (2020) 130, arXiv:2001.08776 [hep-th].
  37. S. Franco and X. Yu, “BFT22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT: a general class of 2d𝒩𝒩\mathcal{N}caligraphic_N = (0, 2) theories, 3-manifolds and toric geometry,” JHEP 08 (2022) 277, arXiv:2107.00667 [hep-th].
  38. S. Franco, A. Mininno, A. M. Uranga, and X. Yu, “Spin(7) orientifolds and 2d 𝒩𝒩\mathcal{N}caligraphic_N = (0, 1) triality,” JHEP 01 (2022) 058, arXiv:2112.03929 [hep-th].
  39. S. Franco, A. Mininno, A. M. Uranga, and X. Yu, “2d 𝒩𝒩\mathcal{N}caligraphic_N = (0, 1) gauge theories and Spin(7) orientifolds,” JHEP 03 (2022) 150, arXiv:2110.03696 [hep-th].
  40. S. Franco, D. Ghim, and R.-K. Seong, “Brane brick models for the Sasaki-Einstein 7-manifolds Yp,k𝑝𝑘{}^{p,k}start_FLOATSUPERSCRIPT italic_p , italic_k end_FLOATSUPERSCRIPT(ℂℂ\mathbb{C}blackboard_Cℙℙ\mathbb{P}blackboard_P11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT× ℂℂ\mathbb{C}blackboard_Cℙℙ\mathbb{P}blackboard_P11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT) and Yp,k𝑝𝑘{}^{p,k}start_FLOATSUPERSCRIPT italic_p , italic_k end_FLOATSUPERSCRIPT(ℂℂ\mathbb{C}blackboard_Cℙℙ\mathbb{P}blackboard_P22{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT),” JHEP 03 (2023) 050, arXiv:2212.02523 [hep-th].
  41. A. Gadde, S. Gukov, and P. Putrov, “(0, 2) trialities,” JHEP 03 (2014) 076, arXiv:1310.0818 [hep-th].
  42. D. Martelli and J. Sparks, “Notes on toric Sasaki-Einstein seven-manifolds and AdS(4) / CFT(3),” JHEP 11 (2008) 016, arXiv:0808.0904 [hep-th].
  43. S. Franco and X. Yu, “Generalized Global Symmetries in Brane Brick Models,” to appear.
  44. N. Reshetikhin and V. G. Turaev, “Invariants of three manifolds via link polynomials and quantum groups,” Invent. Math. 103 (1991) 547–597.
  45. V. G. Turaev and O. Y. Viro, “State sum invariants of 3 manifolds and quantum 6j symbols,” Topology 31 (1992) 865–902.
  46. J. W. Barrett and B. W. Westbury, “Invariants of piecewise linear three manifolds,” Trans. Am. Math. Soc. 348 (1996) 3997–4022, arXiv:hep-th/9311155.
  47. E. Witten, “AdS / CFT correspondence and topological field theory,” JHEP 12 (1998) 012, arXiv:hep-th/9812012.
  48. A. Kirillov, Jr. and B. Balsam, “Turaev-Viro invariants as an extended TQFT,” arXiv:1004.1533 [math.GT].
  49. A. Kapustin and N. Saulina, “Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory,” arXiv:1012.0911 [hep-th].
  50. A. Kitaev and L. Kong, “Models for Gapped Boundaries and Domain Walls,” Commun. Math. Phys. 313 no. 2, (2012) 351–373, arXiv:1104.5047 [cond-mat.str-el].
  51. J. Fuchs, C. Schweigert, and A. Valentino, “Bicategories for boundary conditions and for surface defects in 3-d TFT,” Commun. Math. Phys. 321 (2013) 543–575, arXiv:1203.4568 [hep-th].
  52. D. S. Freed and C. Teleman, “Relative quantum field theory,” Commun. Math. Phys. 326 (2014) 459–476, arXiv:1212.1692 [hep-th].
  53. D. S. Freed and C. Teleman, “Topological dualities in the Ising model,” Geom. Topol. 26 (2022) 1907–1984, arXiv:1806.00008 [math.AT].
  54. D. S. Freed, G. W. Moore, and C. Teleman, “Topological symmetry in quantum field theory,” arXiv:2209.07471 [hep-th].
  55. J. Kaidi, K. Ohmori, and Y. Zheng, “Symmetry TFTs for Non-Invertible Defects,” arXiv:2209.11062 [hep-th].
  56. F. Baume, J. J. Heckman, M. Hübner, E. Torres, A. P. Turner, and X. Yu, “SymTrees and Multi-Sector QFTs,” arXiv:2310.12980 [hep-th].
  57. F. Apruzzi, F. Bonetti, I. García Etxebarria, S. S. Hosseini, and S. Schafer-Nameki, “Symmetry TFTs from String Theory,” arXiv:2112.02092 [hep-th].
  58. M. van Beest, D. S. W. Gould, S. Schafer-Nameki, and Y.-N. Wang, “Symmetry TFTs for 3d QFTs from M-theory,” arXiv:2210.03703 [hep-th].
  59. M. Etheredge, I. Garcia Etxebarria, B. Heidenreich, and S. Rauch, “Branes and symmetries for 𝒩=3𝒩3\mathcal{N}=3caligraphic_N = 3 S-folds,” arXiv:2302.14068 [hep-th].
  60. D. Belov and G. W. Moore, “Holographic Action for the Self-Dual Field,” arXiv:hep-th/0605038.
  61. S. Gukov, P.-S. Hsin, and D. Pei, “Generalized global symmetries of T⁢[M]𝑇delimited-[]𝑀T[M]italic_T [ italic_M ] theories. Part I,” JHEP 04 (2021) 232, arXiv:2010.15890 [hep-th].
  62. M. D. F. de Wild Propitius, Topological interactions in broken gauge theories. PhD thesis, Amsterdam U., 1995. arXiv:hep-th/9511195.
  63. J. Kaidi, E. Nardoni, G. Zafrir, and Y. Zheng, “Symmetry TFTs and Anomalies of Non-Invertible Symmetries,” arXiv:2301.07112 [hep-th].
  64. D. Tambara and S. Yamagami, “Tensor categories with fusion rules of self-duality for finite abelian groups,” Journal of Algebra 209 no. 2, (1998) 692–707. https://www.sciencedirect.com/science/article/pii/S0021869398975585.
  65. J. Kaidi, G. Zafrir, and Y. Zheng, “Non-invertible symmetries of 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM and twisted compactification,” JHEP 08 (2022) 053, arXiv:2205.01104 [hep-th].
  66. V. Bashmakov, M. Del Zotto, A. Hasan, and J. Kaidi, “Non-invertible Symmetries of Class 𝒮𝒮\mathcal{S}caligraphic_S Theories,” arXiv:2211.05138 [hep-th].
  67. Z. Sun and Y. Zheng, “When are Duality Defects Group-Theoretical?,” arXiv:2307.14428 [hep-th].
  68. J. J. Heckman and L. Tizzano, “6D Fractional Quantum Hall Effect,” JHEP 05 (2018) 120, arXiv:1708.02250 [hep-th].
  69. F. Apruzzi, “Higher form symmetries TFT in 6d,” JHEP 11 (2022) 050, arXiv:2203.10063 [hep-th].
  70. Springer Science & Business Media, 2007.
  71. J. Cheeger and J. Simons, “Differential characters and geometric invariants,” 1985. https://api.semanticscholar.org/CorpusID:50800553.
  72. C. Baer and C. Becker, “Differential characters and geometric chains,” 2013.
  73. AMS, Providence, USA, 2003.
  74. P. G. Camara, L. E. Ibanez, and F. Marchesano, “RR photons,” JHEP 09 (2011) 110, arXiv:1106.0060 [hep-th].
  75. M. R. Douglas, “Branes within branes,” NATO Sci. Ser. C 520 (1999) 267–275, arXiv:hep-th/9512077.
  76. K. Roumpedakis, S. Seifnashri, and S.-H. Shao, “Higher Gauging and Non-invertible Condensation Defects,” arXiv:2204.02407 [hep-th].
  77. J. Kaidi, K. Ohmori, and Y. Zheng, “Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories,” Phys. Rev. Lett. 128 no. 11, (2022) 111601, arXiv:2111.01141 [hep-th].
  78. Y. Choi, C. Cordova, P.-S. Hsin, H. T. Lam, and S.-H. Shao, “Noninvertible duality defects in 3+1 dimensions,” Phys. Rev. D 105 no. 12, (2022) 125016, arXiv:2111.01139 [hep-th].
  79. A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics,” Nucl. Phys. B 492 (1997) 152–190, arXiv:hep-th/9611230.
  80. G. Kac, “Finite group rings,” Trans. Moscow Math. Soc. 15 (1966) 251–294.
  81. C. Zhang and C. Córdova, “Anomalies of (1+1)⁢D11𝐷(1+1)D( 1 + 1 ) italic_D categorical symmetries,” arXiv:2304.01262 [cond-mat.str-el].
  82. A. Perez-Lona, D. Robbins, E. Sharpe, T. Vandermeulen, and X. Yu, “Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases,” arXiv:2311.16230 [hep-th].
  83. O. Diatlyk, C. Luo, Y. Wang, and Q. Weller, “Gauging Non-Invertible Symmetries: Topological Interfaces and Generalized Orbifold Groupoid in 2d QFT,” arXiv:2311.17044 [hep-th].
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  1. Xingyang Yu
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