Topological Defect Lines and Renormalization Group Flows in Two Dimensions

TL;DR

This paper explores topological defect lines in two-dimensional conformal field theories, analyzing their crossing relations, anomalies, and role in constraining renormalization group flows to critical points or topological phases.

Contribution

It generalizes the concept of topological defect lines to include non-braided fusion categories and uses them to analyze RG flows and IR phases in 2D CFTs.

Findings

Non-invertible TDLs prevent non-degenerate gapped vacua.

IR TQFTs can be fully determined from TDLs and modular invariance.

Constraints on RG flows from TDLs and anomalies.

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.