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- W2079740443 abstract "We study Nekrasov's deformed partition function $Z(varepsilon_1,varepsilon_2,vec{a};mathfrak q,boldsymbolbeta)$ 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) $F(varepsilon_1,varepsilon_2,vec{a};mathfrak q,boldsymbolbeta) = varepsilon_1varepsilon_2 log Z(varepsilon_1,varepsilon_2,vec{a};mathfrak q,boldsymbolbeta)$ is regular at $varepsilon_1 = varepsilon_2 = 0$ (a part of Nekrasov's conjecture), and (b) the genus $1$ parts, which are first several Taylor coefficients of $F(varepsilon_1,varepsilon_2,vec{a};mathfrak q,boldsymbolbeta)$, are written explicitly in terms of $tau = d^2 F(0,0,vec{a};mathfrak q,boldsymbolbeta)/da^2$ in rank $2$ case." @default.
- W2079740443 created "2016-06-24" @default.
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- W2079740443 date "2005-12-01" @default.
- W2079740443 modified "2023-10-12" @default.
- W2079740443 title "Instanton counting on blowup. II. K-theoretic partition function" @default.
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- W2079740443 doi "https://doi.org/10.1007/s00031-005-0406-0" @default.
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