Topological Defect Lines and Renormalization Group Flows in Two Dimensions
Abstract
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.
Cite
@article{arxiv.1802.04445,
title = {Topological Defect Lines and Renormalization Group Flows in Two Dimensions},
author = {Chi-Ming Chang and Ying-Hsuan Lin and Shu-Heng Shao and Yifan Wang and Xi Yin},
journal= {arXiv preprint arXiv:1802.04445},
year = {2019}
}
Comments
101 pages, 63 figures, 2 tables; v3: minor changes, added footnotes and references, published version