Lectures on Instanton Counting

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dc.creatorNakajima, Hiraku
dc.creatorYoshioka, Kota
dc.date2003-11-05
dc.date.accessioned2026-07-07T05:02:37Z
dc.date.available2026-07-07T05:02:37Z
dc.descriptionThese notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vecτ)$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$. The second is review of geometry of the Seiberg-Witten curves and the geometric engineering of the gauge theory, which are physical backgrounds of Nekrasov's partition functions. The first part is continuation of math.AG/0306198, where we identified the Seiberg-Witten prepotential with $Z(0,0,\vec{a};\q,0)$. We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten $u$-plane. We also determine the coefficients of $\ve_1\ve_2$ and $(\ve_1^2+\ve_2^2)/3$ (the genus 1 part) of the partition function, which coincide with two measure factors $A$, $B$ appeared in the $u$-plane integral. The proof is based on the blowup equation which we derived in the previous paper.
dc.description60 pages, to appear in Proceedings of "Workshop on algebraic structures and moduli spaces", July 14 - 20, 2003, Centre de recherches mathematiques, Universite de Montreal
dc.identifierhttps://arxiv.org/abs/math/0311058
dc.identifierhttp://arxiv.org/abs/math/0311058
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69079
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleLectures on Instanton Counting
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