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

• 成果类型: Article
• 署名作者: Nakajima, H; Yoshioka, K
• 署名单位: Kyoto University; Kobe University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-005-0444-1
• 发表日期: 2005
• 页码: 313-355
• 关键词: s-duality conjecture; donaldson polynomial invariants; kac-moody algebras; quiver varieties; whitham hierarchies; hilbert scheme; K-THEORY; formulas; witten; MODULI

摘要

We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on R-4 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 R-4, 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.