Mixed global anomalies and boundary conformal field theories

TL;DR

This paper explores how mixed global gauge-gravitational anomalies in WZW models influence boundary conformal field theories, revealing conditions on model levels and boundary states related to the symmetries of simple Lie groups.

Contribution

It establishes a connection between mixed anomalies and boundary conditions in WZW models, providing new insights into symmetry constraints and anomaly cancellation conditions.

Findings

Mixed anomalies prevent orbifolding by the center.

Conditions on WZW levels ensure anomaly cancellation.

Boundary states invariant under symmetries impose similar constraints.

Abstract

We consider the relation of mixed global gauge gravitational anomalies and boundary conformal field theory in WZW models for simple Lie groups. The discrete symmetries of consideration are the centers of the simple Lie groups. These mixed anomalies prevent to gauge them i.e, take the orbifold by the center. The absence of anomalies impose conditions on the levels of WZW models. Next, we study the conformal boundary conditions for the original theories. We consider the existence of a conformal boundary state invariant under the action of the center. This also gives conditions on the levels of WZW models. By considering the combined action of the center and charge conjugation on boundary states, we reproduce the condition obtained in the orbifold analysis.