Equivariant volumes of non-compact quotients and instanton counting

Preprint English OPEN
Martens, Johan (2006)
  • Related identifiers: doi: 10.1007/s00220-008-0501-x
  • Subject: Mathematics - Symplectic Geometry | 53Z05 | 53D20 | High Energy Physics - Theory | Mathematics - Algebraic Geometry
    arxiv: High Energy Physics::Theory | Mathematics::Symplectic Geometry

Motivated by Nekrasov's instanton counting, we discuss a method for calculating equivariant volumes of non-compact quotients in symplectic and hyper-K\"ahler 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.
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