Multi instanton calculus on ALE spaces

Details Multi instanton calculus on ALE spaces Multi instanton calculus on ALE spaces

2004-06-25

arxiv.org/abs/hep-th/0406243v2

Nucl.Phys. B703 (2004) 518-536

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, few explanations added. version to appear in nucl.phys

Scientific paper

10.1016/j.nuclphysb.2004.09.014

We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric ${\cal N}=2, 2^*$ gauge theories on ALE spaces of the $A_n$ type. Furthermore we derive the Poincar\'{e} polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the ${\cal N}=4$ partition function which is a modular form in agreement with the expectations of $SL(2,\Z)$ duality.

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