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

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 ' 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 ' due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The eta ' term plays a substantial role in exploring the emergent higher-group structure at low energies.

Automated summary

In this study, we discuss the BCF anomaly of massless QCD-like theories, initially obtained by Anber and Poppitz, from the perspective of low energy effective theories. We assume that these theories undergo spontaneous chiral symmetry breaking due to a quark bilinear condensate. By utilizing the 't Hooft anomaly matching condition for the BCF anomaly, we demonstrate that the low energy effective action comprises a chiral Lagrangian, a Wess-Zumino-Witten term, and an interaction term between the eta' meson and the background gauge field for a discrete one-form symmetry. We show that the low energy effective action resolves the quantum inconsistencies associated with the eta' meson, arising from the ambiguity of uplifting the action to a five-dimensional spacetime with a boundary. The eta' term plays a significant role in exploring the emergent higher-group structure at low energies.