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

By H. Nakajima, K. Yoshioka. 2005

169 citations recorded by the source corpus.

AbstractWe study Nekrasov's deformed partition function $Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ 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) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ 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 $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$, are written explicitly in terms of $\tau = d^2 F(0,0,\vec{a};\mathfrak q,\boldsymbol\beta)/da^2$ in rank $2$ case.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c17554260aad4032b8329b5d4fa63005b1066626

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In Geometry and Topology

  1. Amer Iqbal
  2. C. Vafa
  3. C. Kozçaz
  4. H. Awata
  5. Y. Yamada
  6. Marcos Mariño
  7. K. Hori
  8. Mina Aganagic

In Nuclear and High Energy Physics

  1. C. Vafa
  2. C. Kozçaz
  3. Amer Iqbal
  4. H. Awata
  5. Marcos Mariño
  6. Masato Taki
  7. Y. Yamada
  8. Mina Aganagic

In Statistical and Nonlinear Physics

  1. C. Vafa
  2. C. Kozçaz
  3. Amer Iqbal
  4. H. Awata
  5. Marcos Mariño
  6. Y. Yamada
  7. Masato Taki
  8. Mina Aganagic

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