The Spectrum of Yang Mills on a Sphere

TL;DR

This paper analyzes the representation content of free large N SU(N) Yang Mills theory on a sphere by decomposing its thermal partition function into conformal group characters, and extends the method to N=4 Super Yang Mills.

Contribution

It introduces a method to determine the representation content of Yang Mills theories on a sphere using partition function decomposition, including N=4 Super Yang Mills.

Findings

Decomposition of the thermal partition function into SO(4,2) characters.

Extension of the method to N=4 Super Yang Mills.

Insights into the spectrum of Yang Mills theories on curved backgrounds.

Abstract

In this note, we determine the representation content of the free, large N, SU(N) Yang Mills theory on a sphere by decomposing its thermal partition function into characters of the irreducible representations of the conformal group SO(4,2). We also discuss the generalization of this procedure to finding the representation content of N=4 Super Yang Mills.