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

TL;DR

This paper demonstrates how to compute equivariant Donaldson invariants of compact toric surfaces using residues of Virasoro conformal blocks, leveraging the AGT correspondence between gauge theories and conformal field theories.

Contribution

It establishes a novel connection between Donaldson invariants and conformal field theory computations via the AGT correspondence.

Findings

Equivariant Donaldson polynomials can be expressed as residues of conformal blocks.

The method applies to compact toric surfaces.

Provides a new computational approach linking gauge theory and CFT.

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.