Nonabelian localization for gauge theory on the fuzzy sphere

TL;DR

This paper uses nonabelian equivariant localization to compute the partition function of Yang-Mills theory on the fuzzy sphere, explicitly evaluating saddle-point contributions and recovering the classical case in the commutative limit.

Contribution

It introduces a novel application of nonabelian localization techniques to gauge theory on fuzzy geometries, providing explicit saddle-point evaluations.

Findings

Partition function expressed as sum over critical points

Explicit evaluation of classical saddle-point contributions

Recovers ordinary Yang-Mills results in the commutative limit

Abstract

We apply nonabelian equivariant localization techniques to Yang-Mills theory on the fuzzy sphere to write the partition function entirely as a sum over local contributions from critical points of the action. The contributions of the classical saddle-points are evaluated explicitly, and the partition function of ordinary Yang-Mills theory on the sphere is recovered in the commutative limit.