High Energy Theory Seminar

Global symmetries in two dimensions are implemented by topological defect lines (TDLs).  For continuous global symmetries, the TDLs are nothing but the Noether charges.  However, there are TDLs that are not associated to any global symmetry, and can be thought of as a generalized notion of symmetry.  We study the crossing relations of TDLs and use them to constrain renormalization group flows in two dimensions. We show that if certain non-symmetry TDLs are preserved along a flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we bootstrap all the OPE coefficients in the infrared TQFTs from the consideration of TDLs together with modular invariance.