BCF anomaly and higher-group structure in the low energy effective theories of mesons

TL;DR

This paper analyzes the BCF anomaly in massless QCD-like theories, revealing how the low energy effective action, including the $ ext{ exteta}^ extprime$ meson interactions, cancels quantum inconsistencies and uncovers higher-group structures.

Contribution

It demonstrates the role of the $ ext{ exteta}^ extprime$ meson in the low energy effective theory and elucidates the emergent higher-group structure related to the BCF anomaly.

Findings

The low energy effective action includes a chiral Lagrangian, Wess-Zumino-Witten term, and $ ext{ exteta}^ extprime$ interactions.

The $ ext{ exteta}^ extprime$ term cancels quantum inconsistencies in the anomaly.

Emergent higher-group structures are revealed at low energies.

Abstract

We discuss the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to a quark bilinear condensate. Using the 't Hooft anomaly matching condition for the BCF anomaly, we find that the low energy effective action is composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an interaction term of the $\eta^\prime$ meson with the background gauge field for a discrete one-form symmetry. It is shown that the low energy effective action cancels the quantum inconsistencies associated with $\eta^\prime$ due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The $\eta^\prime$ term plays a substantial role in exploring the emergent higher-group structure at low energies.