Instanton Calculus and Loop Operator in Supersymmetric Gauge Theory

TL;DR

This paper uses instanton calculus and free fermion formalism to compute the glueball loop operator in supersymmetric gauge theory, achieving exact results that match previous generating function calculations.

Contribution

It introduces an exact method to compute chiral correlators in supersymmetric gauge theory using localization and free fermion techniques.

Findings

Exact summation of contributions from fixed points labeled by Young diagrams.

Laplace transform of the loop operator matches known generating functions.

Demonstrates the effectiveness of instanton calculus in supersymmetric gauge theories.

Abstract

We compute one-point function of the glueball loop operator in the maximally confining phase of supersymmetric gauge theory using instanton calculus. In the maximally confining phase the residual symmetry is the diagonal U(1) subgroup and the localization formula implies that the chiral correlation functions are the sum of the contributions from each fixed point labeled by the Young diagram. The summation can be performed exactly by operator formalism of free fermions, which also featured in the equivariant Gromov-Witten theory of P^1. By taking the Laplace transformation of the glueball loop operator, we find an exact agreement with the previous results for the generating function (resolvent) of the glueball one-point functions.