Between Symmetry and Duality in Supersymmetric Quantum Field Theories

We study two cases of interrelations between the enhancement of symmetries in the infrared (IR) and duality properties of supersymmetric quantum field theories in four dimensions. First, we discuss an SU(2) N = 1 model with four flavors, singlet fields, and a superpotential. We show that this model flows to a conformal field theory with E-6 x U(1) global symmetry. The enhancement of the flavor symmetry follows from Seiberg duality. The second example is concerned with an SU(4) gauge theory with matter in the fundamental and antisymmetric representations. We argue that this model has enhanced SO(12) symmetry in the IR, and, guided by this enhancement, we deduce a new IR duality.