Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants

Abstract

We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between N = 2 supersymmetric gauge theories and two-dimensional conformal field theory.

arXiv commentTalk presented by A.T. at the conference "Interactions between Geometry and Physics", in honor of Ugo Bruzzo's 60th birthday 17-22 August 2015, Guarujá, São Paulo, Brasil, mostly based on [arXiv:1411.2762] and [arXiv:1509.00267]. 13 pages. Version published in Journal of Geometry and Physics

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• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Gauge theories on compact toric manifolds
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• Super Yang-Mills on Branched Covers and Weighted Projective Spaces
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• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
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