RG flows from WZW models

TL;DR

This paper investigates the renormalization group flows from WZW models of types A, B, C, D, E, proposing criteria for massless and massive flows, and analyzing interface conditions, anomalies, and ground state degeneracies.

Contribution

It introduces a conjecture relating half-integral conditions to simple flows and clarifies the role of anomalies in identifying Verlinde lines.

Findings

Positive couplings lead to massless flows; negative couplings lead to massive flows.

The interface with the half-integral condition obeys double braiding relations.

Ground state degeneracies are computed in the massive phase.

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.