Equivalence of large-$N$ gauge theories on a group manifold and its coset space

TL;DR

This paper generalizes the large-$N$ reduction principle, showing that large-$N$ gauge theories on group manifolds are equivalent to theories on their coset spaces, extending previous results on volume independence.

Contribution

It demonstrates the equivalence of large-$N$ gauge theories on group manifolds and their coset spaces, broadening the understanding of volume independence in gauge theories.

Findings

Large-$N$ gauge theories on group manifolds are equivalent to theories on coset spaces.

The result generalizes previous large-$N$ reduction on flat spaces.

Supports the idea of volume independence in gauge theories.

Abstract

It was shown in arXiv:0912.1456 that the large-$N$ reduction holds on group manifolds in the sense that a large-$N$ gauge theory on a group manifold is realized by a matrix model which is obtained by dimensionally reducing the original theory to zero dimension. In this note, generalizing the above statement, we show that a large-$N$ gauge theory on a group manifold is equivalent to a theory which is obtained by reducing the original theory to its coset space. This is analogous to the statement of the large-$N$ reduction on flat spaces that large-$N$ gauge theories are independent of the volume.