General anomaly matching by Goldstone bosons

TL;DR

This paper demonstrates how Goldstone bosons from spontaneous symmetry breaking can nonperturbatively reproduce UV anomalies using a generalized framework involving Wess-Zumino-Witten terms and invertible field theories.

Contribution

It provides a general definition of Wess-Zumino-Witten terms via invertible field theories and explores their role in anomaly matching through Goldstone bosons.

Findings

Goldstone bosons can reproduce UV anomalies nonperturbatively.

A new framework for defining Wess-Zumino-Witten terms using invertible field theories.

Application to ${ m SO}(N_c)$ QCD-like theories in four dimensions.

Abstract

We describe how Goldstone bosons of spontaneous symmetry breaking $G \to H$ can reproduce anomalies of UV theories under the symmetry group $G$ at the nonperturbative level. This is done by giving a general definition of Wess-Zumino-Witten terms in terms of the invertible field theories in $d+1$ dimensions which describe the anomalies of $d$-dimensional UV theories. The hidden local symmetry $\widehat H$, which is used to describe Goldstone bosons in coset construction $G/H$, plays an important role. Our definition also naturally leads to generalized $\theta$-angles of the hidden local gauge group $\widehat H$. We illustrate this point by ${\rm SO}(N_c)$ (or ${\rm Spin}(N_c)$) QCD-like theories in four dimensions.