General anomaly matching by Goldstone bosons

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 $\hat{H}$, 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 $\hat{H}$. We illustrate this point by $\mathrm{SO}(N_c)$ (or $\mathrm{Spin}(N_c)$) QCD-like theories in four dimensions.

19 pages, 2 figures; V2: minor corrections and references added; V3: minor improvement

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