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Article

Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants

Journal of High Energy Physics. 2016. No. 723. P. 39.
Bershtein M., Bonelli G., Tanzini A., Ronzani M.

We provide a contour integral formula for the exact partition function of  N=2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N=2* theory on P^2 for all instanton numbers. In the zero mass case, corresponding to the N=4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of quasi-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.