The chiral ring and the periods of the resolvent

Abstract

The strongly coupled vacua of an N = 1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N = 2 Seiberg–Witten curve (the so-called strong-coupling approach). We show that these conditions are equivalent to the existence of certain relations in the chiral ring, which themselves follow from the fact that the gauge group has a finite rank. This provides a conceptually very simple explanation of why and how the strongly coupled physics of N = 1 theories, including fractional instanton effects, chiral symmetry breaking and confinement, can be derived from purely semi-classical calculations involving instantons only.