Patterns of Duality in N=1 SUSY Gauge Theories

Abstract

We study the patterns in the duality of a wide class of N=1 supersymmetric gauge theories in four dimensions. We present many new generalizations of the classic duality models of Kutasov and Schwimmer, which have themselves been generalized numerous times in works of Intriligator, Leigh and the present authors. All of these models contain one or two fields in a two-index tensor representation, along with fields in the defining representation. The superpotential for the two-index tensor(s) resembles A_k or D_k singularity forms, generalized from numbers to matrices. Looking at the ensemble of these models, classifying them by superpotential, gauge group, and ``level'' -- for terminology we appeal to the architecture of a typical European-style theatre -- we identify emerging patterns and note numerous interesting puzzles.