General anomaly matching by Goldstone bosons

Abstract

We describe how Goldstone bosons of spontaneous symmetry breaking G → H can reproduce anomalies of UV theories under the symmetry group G at the nonpertur- bative 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 Ĥ , which is used to describe Goldstone bosons in coset construction G/H , plays an important role. Our definition also naturally leads to generalized θ-angles of the hidden local gauge group Ĥ. We illustrate this point by SO(Nc) (or Spin(Nc)) QCD-like theories in four dimensions.