Wall Crossing and Instantons in Compactified Gauge Theory
Heng-Yu Chen, Nick Dorey, Kirill Petunin
TL;DR
This paper computes the leading instanton effects on the moduli space metric of a compactified supersymmetric gauge theory, confirming recent conjectures related to wall-crossing phenomena.
Contribution
It provides a precise calculation of instanton contributions in N=2 SU(2) gauge theory on R^3 x S^1, supporting the conjectured exact metric.
Findings
Agreement with the semiclassical expansion of the exact metric
Validation of wall-crossing predictions in the compactified theory
Explicit instanton contribution calculation
Abstract
We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.
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