, Volume 162, Issue 2, pp 313-355
Date: 14 Jun 2005

Instanton counting on blowup. I. 4-dimensional pure gauge theory

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Abstract

We give a mathematically rigorous proof of Nekrasov’s conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on ℝ4 gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of ℝ4, we derive a differential equation for the Nekrasov’s partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al.

Mathematics Subject Classification (2000)

14D21, 57R57, 81T13, 81T60