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

TitleExact results for N=2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
Publication TypeJournal Article
Year of Publication2016
AuthorsBershtein, M, Bonelli, G, Ronzani, M, Tanzini, A
JournalJournal of High Energy Physics
Volume2016
Pagination23
Date PublishedJul
ISSN1029-8479
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.

URLhttps://doi.org/10.1007/JHEP07(2016)023
DOI10.1007/JHEP07(2016)023

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