Abstract
We prove that the K-theoretic Nekrasov instanton partition functions have a positive radius of convergence in the instanton counting parameter and are holomorphic functions of the Coulomb parameters in a suitable domain. We discuss the implications for the AGT correspondence and the analyticity of the norm of Gaiotto states for the deformed Virasoro algebra. The proof is based on random matrix techniques and relies on an integral representation of the partition function, due to Moore, Nekrasov, and Shatashvili, which we also prove.
Highlights
The purpose of this paper is to study the analytic properties of the Nekrasov instanton partition function
The instanton partition function is the non-perturbative contribution of instantons to a gauge theory in an -background
The torus is a product of a two-dimensional torus acting on the projective plane and a torus acting on the framing
Summary
The purpose of this paper is to study the analytic properties of the Nekrasov instanton partition function. In N = 2 supersymmetric gauge theory in four and five dimensions, Nekrasov’s instanton partition function [18] plays the role of a basic building block. The instanton partition function is the non-perturbative contribution of instantons to a gauge theory in an -background. It is the generating function of integrals of torus equivariant cohomology classes (K - theory classes in the five dimensional theory) on the moduli space of framed torsion free sheaves with fixed rank on the complex projective plane. The parameters 1, 2 of the -background are the equivariant parameters of the twodimensional torus in the mathematical description and serve as an infrared regulator
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