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

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

2003-06-12

arxiv.org/abs/math/0306198v2

Mathematics

Algebraic Geometry

Title is changed. Introduction is expanded. A section on Seiberg-Witten prepotential is added. Accepted for publication in Inv

Scientific paper

We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$ 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 $\mathbb R^4$, 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.

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