Inventiones mathematicae

, Volume 162, Issue 2, pp 313-355

First online:

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

  • Hiraku NakajimaAffiliated withDepartment of Mathematics, Kyoto University Email author 
  • , Kota YoshiokaAffiliated withDepartment of Mathematics, Faculty of Science, Kobe University Email author 

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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.