The Chiral Ring and the Periods of the Resolvent

TL;DR

This paper links the strong-coupling dynamics of N=1 supersymmetric gauge theories to chiral ring relations, showing that non-perturbative phenomena like confinement can be understood through semi-classical instanton calculations.

Contribution

It demonstrates the equivalence between period quantization conditions and chiral ring relations, simplifying the understanding of strongly coupled N=1 gauge theories.

Findings

Strong-coupling vacua characterized by period quantization

Chiral ring relations encode non-perturbative effects

Semi-classical instanton calculations reproduce confinement phenomena

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.