Holomorphic Anomaly in Gauge Theory on ALE space

TL;DR

This paper explores the holomorphic anomaly in Omega-deformed N=2 supersymmetric SU(2) gauge theory on ALE space, connecting partition functions with special geometry, anomaly equations, and refined topological string theory.

Contribution

It introduces a novel analysis of the holomorphic anomaly in gauge theory on ALE space and links it to refined topological string theory interpretations.

Findings

Partition functions are reproduced via special geometry and anomaly equations.

Boundary conditions at monopole/dyon points are expressed through Schwinger integrals.

A connection between 4D gauge theory and 5D topological string theory on ALE space is proposed.

Abstract

We consider four-dimensional Omega-deformed N=2 supersymmetric SU(2) gauge theory on A1 space and its lift to five dimensions. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation. Schwinger type integral expressions for the boundary conditions at the monopole/dyon point in moduli space are inferred. The interpretation of the five-dimensional partition function as the partition function of a refined topological string on A1x(local P1xP1) is suggested.