Equivariant volumes of non-compact quotients and instanton counting

Johan Martens*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by Nekrasov's instanton counting, we discuss a method for calculating equivariant volumes of non-compact quotients in symplectic and hyper-Kahler geometry by means of the Jeffrey-Kirwan residue formula of non-abelian localization. In order to overcome the non-compactness, we use varying symplectic cuts to reduce the problem to a compact setting, and study what happens in the limit that recovers the original problem. We implement this method for the ADHM construction of the moduli spaces of framed Yang-Mills instantons on R-4 and rederive the formulas for the equivariant volumes obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated residues of a single rational function.

Original languageEnglish
Pages (from-to)827-857
Number of pages31
JournalCommunications in Mathematical Physics
Volume281
Issue number3
DOIs
Publication statusPublished - Aug 2008

Keywords

  • COHOMOLOGY
  • AFFINE LIE-ALGEBRAS
  • RESIDUE
  • RANK
  • WHITTAKER VECTORS
  • CO-HOMOLOGY
  • BLOWUP
  • GEOMETRIC INVARIANT-THEORY
  • MOMENT MAP
  • LOCALIZATION FORMULA

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