Instanton counting on blowup. II: \(K\)-theoretic partition function

DOI10.1007/S00031-005-0406-0zbMATH Open1110.14015arXivmath/0505553OpenAlexW2079740443MaRDI QIDQ849850

Author name not available (Why is that?)

Publication date: 1 November 2006

Published in: (Search for Journal in Brave)

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

m a t h b b 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

e p s i l o n_{1} e p s i l o n_{2}

is regular at

e p s i l o n_{1} = e p s i l o n_{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.

Full work available at URL: https://arxiv.org/abs/math/0505553

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