Instanton counting on blowup. II. K-theoretic partition function

May, 2005
26 pages
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Abstract:
We study Nekrasov's deformed partition function of 5-dimensional supersymmetric Yang-Mills theory compactified on a circle. Mathematically it is the generating function of the characters of the coordinate rings of the moduli spaces of instantons on R4\mathbb R^4. We show that it satisfies a system of functional equations, called blowup equations, whose solution is unique. As applications, we prove (a) logarithm of the partition function times ϵ1ϵ2\epsilon_1\epsilon_2 is regular at ϵ1=ϵ2=0\epsilon_1 = \epsilon_2 = 0, (a part of Nekrasov's conjecture), and (b) the genus 1 parts, which are first several Taylor coefficients of the logarithm of the partition function, are written explicitly in terms of the Seiberg-Witten curves in rank 2 case.
Note:
  • Dedicated to Vladimir Drinfeld on his 50th birthday
  • gauge field theory: Yang-Mills
  • supersymmetry
  • dimension: 5
  • partition function: deformation
  • K-theory
  • instanton
  • correlation function