Nekrasov Functions from Exact BS Periods: the Case of SU(N)

TL;DR

This paper demonstrates that Nekrasov functions with one deformation parameter can be derived from exact Seiberg-Witten periods by replacing the differential with its quantized version, confirmed through perturbative checks for SU(N).

Contribution

It provides an explicit formulation connecting Nekrasov functions to quantized Seiberg-Witten periods, extending previous conjectures with concrete first-order verifications.

Findings

Confirmed the quantized Seiberg-Witten approach at first order in ^2.

Validated the method in the instanton expansion for SU(N).

Established consistency of the deformed Seiberg-Witten equations.

Abstract

In arXiv:0910.5670 we suggested that the Nekrasov function with one non-vanishing deformation parameter \epsilon is obtained by the standard Seiberg-Witten contour-integral construction. The only difference is that the Seiberg-Witten differential pdx is substituted by its quantized version for the corresponding integrable system, and contour integrals become exact monodromies of the wave function. This provides an explicit formulation of the earlier guess in arXiv:0908.4052. In this paper we successfully check this suggestion in the first order in \epsilon^2 and the first order in instanton expansion for the SU(N) model, where non-trivial is already consistency of the so deformed Seiberg-Witten equations.