Deformations of W A,D,E SCFTs

Abstract

We discuss aspects of theories with superpotentials given by Arnold’s A, D, E singularities, particularly the novelties that arise when the fields are matrices. We focus on 4d N= 1 variants of susy QCD, with U(Nc) or SU(Nc) gauge group, Nf fundamental flavors, and adjoint matter fields X and Y appearing in WA,D,E(X, Y) superpotentials. Many of our considerations also apply in other possible contexts for matrix-variable WA,D,E. The 4d WA,D,E SQCD-type theories RG flow to superconformal field theories, and there are proposed duals in the literature for the WAk, WDk, and WE7 cases. As we review, the WDeven and WE7 duals rely on a conjectural, quantum truncation of the chiral ring. We explore these issues by considering various deformations of the WA,D,E superpotentials, and the resulting RG flows and IR theories. Rather than finding supporting evidence for the quantum truncation and WDeven and WE7 duals, we note some challenging evidence to the contrary.