Abstract
We discuss two-dimensional conformal field theories (CFTs) which are invariant under gauging a non-invertible global symmetry. At every point on the orbifold branch of c = 1 CFTs, it is known that the theory is self-dual under gauging a ℤ2 × ℤ2 symmetry, and has Rep(H8) and Rep(D8) fusion category symmetries as a result. We find that gauging the entire Rep(H8) fusion category symmetry maps the orbifold theory at radius R to that at radius 2/R. At R = \( \sqrt{2} \), which corresponds to two decoupled Ising CFTs (Ising2 in short), the theory is self-dual under gauging the Rep(H8) symmetry. This implies the existence of a topological defect line in the Ising2 CFT obtained from half-space gauging of the Rep(H8) symmetry, which commutes with the c = 1 Virasoro algebra but does not preserve the fully extended chiral algebra. We bootstrap its action on the c = 1 Virasoro primary operators, and find that there are no relevant or marginal operators preserving it. Mathematically, the new topological line combines with the Rep(H8) symmetry to form a bigger fusion category which is a ℤ2-extension of Rep(H8). We solve the pentagon equations including the additional topological line and find 8 solutions, where two of them are realized in the Ising2 CFT. Finally, we show that the torus partition functions of the Monster2 CFT and Ising×Monster CFT are also invariant under gauging the Rep(H8) symmetry.
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Acknowledgments
We are grateful to P.-S. Hsin, T. Jacobson, B. C. Rayhaun, Y. Sanghavi, S. Seifnashri, S.-H. Shao, Y. Wang, Y.-Z. You, C. Zhang, and Y. Zheng for interesting discussions. We also thank TASI 2023: Aspects of Symmetry, PiTP 2023: Understanding Confinement, and PSSCMP 2023: Fractionalization, Criticality and Unconventional Quantum Materials summer schools for providing stimulating environments, where this work was initiated. D.C.L. is supported by the National Science Foundation (NSF) Grant No. DMR-2238360. Z.S. is partially supported by the US Department of Energy (DOE) under cooperative research agreement DE-SC0009919, Simons Foundation award No. 568420 (K.I.), and the Simons Collaboration on Global Categorical Symmetries.
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Choi, Y., Lu, DC. & Sun, Z. Self-duality under gauging a non-invertible symmetry. J. High Energ. Phys. 2024, 142 (2024). https://doi.org/10.1007/JHEP01(2024)142
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DOI: https://doi.org/10.1007/JHEP01(2024)142