Inventiones mathematicae

, Volume 162, Issue 2, pp 313–355 | Cite as

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

  • Hiraku Nakajima
  • Kota Yoshioka


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.


Differential Equation Gauge Theory Partition Function Modulus Space Rigorous Proof 
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© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Department of Mathematics, Faculty of ScienceKobe UniversityKobeJapan

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