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

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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 $\mathbb R^4$. 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 $ε_1ε_2$ is regular at $ε_1 = ε_2 = 0$, (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.
26 pages, no figures

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Algebraic Geometry, High Energy Physics - Theory, Primary 14D21; Secondary 57R57, 81T13, 81T60

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http://salesiana.dossiersoluciones.com/handle/123456789/75318

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505553
 http://arxiv.org/abs/math/0505553

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arXiv