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

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 ${\mathbb{R}}^4$. 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 ${\epsilon }_1{\epsilon }_2$ is regular at ${\epsilon }_1={\epsilon }_2=0$, (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.

26 pages, no figures

References in corpus (2)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• The uses of Whitham hierarchies

Cited by in corpus (21)

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• Seiberg-Witten theory and matrix models
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• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• Construction and Deconstruction of Single Instanton Hilbert Series
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
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• Blowup Equations for Little Strings
• 3d N=2 Chern-Simons-matter theory, Bethe ansatz, and quantum K-theory of Grassmannians
• Holomorphic Anomaly in Gauge Theory on ALE space
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• Towards a gauge theory interpretation of the real topological string
• A projection formula for the ind-Grassmannian