RG flows from WZW models

TL;DR

This work constrains RG flows from ABCDE-type WZW models deformed by adjoint primaries, introducing a half-integral condition that governs the fate of surviving Verlinde lines and enforces a double braiding relation at simple fixed points. By combining anomaly matching, center symmetries, and braiding data with Cardy-type analyses for massive flows, it provides a comprehensive set of explicit massless and massive flow examples across all ADE families, highlighting when IR theories are massless CFTs, TQFTs, or emergent-modular categories. A central conjecture posits that simple RG flows preserve half-integral sums h^UV_j + h^IR_j ∈ 1/2 Z for surviving Verlinde objects, which, if true, explains when certain previously allowed massless flows are ruled out as non-simple and constrains the structure of IR symmetry categories. The results have broad implications for RCFTs and their RG interfaces, connecting 't Hooft anomalies, non-invertible symmetries, and ground-state degeneracies to predict IR behavior in a wide class of two-dimensional theories with potential experimental relevance in systems with SU(N) symmetry.

Abstract

We constrain renormalization group flows from $ABCDE$ type Wess-Zumino-Witten models triggered by adjoint primaries. We propose positive Lagrangian coupling leads to massless flow and negative to massive. In the conformal phase, we prove an interface with the half-integral condition obeys the double braiding relations. Distinguishing simple and non-simple flows, we conjecture the former satisfies the half-integral condition. If the conjecture is true, some previously allowed massless flows are ruled out. For $A$ type, known mixed anomalies fix the ambiguity in identifications of Verlinde lines; an object is identified with its charge conjugate. In the massive phase, we compute ground state degeneracies.