@article {Bershtein2016, title = {Exact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants}, journal = {Journal of High Energy Physics}, volume = {2016}, number = {7}, year = {2016}, month = {Jul}, pages = {23}, abstract = {

We provide a contour integral formula for the exact partition function of $\mathcal{N}=2$ 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 $U(2)\; \mathcal{N}=2^\star$ theory on $\mathbb{P}^2$ for all instanton numbers. In the zero mass case, corresponding to the $\mathcal{N}=4$ supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-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 longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new.

}, issn = {1029-8479}, doi = {10.1007/JHEP07(2016)023}, url = {https://doi.org/10.1007/JHEP07(2016)023}, author = {Mikhail Bershtein and Giulio Bonelli and Massimiliano Ronzani and Alessandro Tanzini} }