Instanton counting on blowup. II. K-theoretic partition function
Instanton counting on blowup. II. K-theoretic partition function
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DOI：
10.1007/s00031-005-0406-0
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发表时间：
2005-05
影响因子：
0.7
通讯作者：
H. Nakajima;K. Yoshioka
中科院分区：
文献类型：
--
作者：
H. Nakajima;K. Yoshioka
研究了紧化在圆上的5维超对称Yang-Mills理论的Nekrasov变形配分函数。在数学上，它是实例的模空间的坐标环的特征的生成函数。我们证明它满足一个泛函方程组，称为爆破方程，其解是唯一的。作为应用，我们证明了(a) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$在（Nekrasov猜想的一部分）上是正则的，(b)属部分是的前几个泰勒系数，它们被显式地用秩格形式表示。
We study Nekrasov's deformed partition functionof 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. We show that it satisfies a system of functional equations, called blowup equations, whose solution is unique. As applications, we prove (a) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ is regular at(a part of Nekrasov's conjecture), and (b) the genusparts, which are first several Taylor coefficients of, are written explicitly in terms ofin rankcase.