Discrete Anomaly Matching for the Pouliot Type Dualities

Abstract

We compute the 't Hooft anomalies of discrete symmetries in the Pouliot type dual theories and check their anomaly matching conditions. The Pouliot type dual theories we will consider in this paper are two dual pairs; the dual pair of ${\cal N}=1$ supersymmetric theories of a $Spin(7)$ gauge theory with spinors and a $SU(N_f-4)$ gauge theory with a symmetric tensor, fundamentals and singlets, and the other dual pair of ${\cal N}=1$ supersymmetric theories of a $Spin(10)$ gauge theory with a spinor and vectors and a $SU(N_f-5)$ gauge theory with a symmetric tensor, fundamentals and singlets. We will show that the both pairs satisfy the discrete anomaly matching conditions.