Mixed global anomalies and boundary conformal field theories

TL;DR

This paper analyzes mixed 't Hooft anomalies between large diffeomorphisms and center symmetries in WZW models for simple Lie groups, identifying how anomaly absence constrains the level $k$ and enables orbifold constructions by the center. It then develops a boundary conformal field theory perspective, showing that the existence of boundary states invariant under the center (or under the combined action of center and charge conjugation for complex representations) mirrors the orbifold consistency conditions. By systematically examining groups A$_{n-1}$, B$_n$, C$_n$, D, E, and exceptional cases, the authors demonstrate a precise correspondence between modular-invariance obstruction in orbifolds and boundary-state invariance. They also illustrate anomaly cancellation in $G\times G'$ setups and discuss subgroup centers, confirming that BCFT criteria reproduce the same anomaly constraints found from orbifold analysis. The work suggests deep links between anomaly classification, orbifold modular invariance, and boundary-state structure with potential implications for SPT phases and higher-dimensional generalizations.

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.

Figures (1)

• Figure 1: The extended Dynkin diagrams and the comarks of the relevant Lie algebras. The symbol $(i;a_{i}^{\vee})$ at each node denotes the label of the corresponding simple root and the comark. Each black node $\bullet$ corresponds to a short root, while each white node $\circ$ corresponds to a long root.