On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit

TL;DR

This paper derives a path integral representation of the Nekrasov instanton partition function for N=2 supersymmetric Yang-Mills theories with fundamental matter and confirms its consistency in the Nekrasov--Shatashvili limit.

Contribution

It introduces a novel path integral formulation of the full instanton partition function and verifies its correctness in the thermodynamic limit.

Findings

Path integral expression matches saddle-point equations in the Nekrasov--Shatashvili limit.

Provides a new analytical tool for studying supersymmetric gauge theories.

Confirms the consistency of the path integral approach with existing methods.

Abstract

In this work we study the Nekrasov--Shatashvili limit of the Nekrasov instanton partition function of Yang--Mills field theories with ${\cal N}=2$ supersymmetry and gauge group SU(N). The theories are coupled with fundamental matter. A path integral expression of the full instanton partition function is derived. It is checked that in the Nekrasov--Shatashvili (thermodynamic) limit the action of the field theory obtained in this way reproduces exactly the equation of motion used in the saddle-point calculations.