Multi instanton calculus on ALE spaces


Abstract in English

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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