Topological defect lines and renormalization group flows in two dimensions
Chi-Ming Chang (Center for Quantum Mathematics and Physics (QMAP), University of California, Davis, CA, 95616, U.S.A.); Ying-Hsuan Lin (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, 91125, U.S.A.); Shu-Heng Shao (School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.); Yifan Wang (Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, U.S.A.); Xi Yin (Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, U.S.A.)
We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the ’t Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.
