Quite a Character: The Spectrum of Yang-Mills on S^3

TL;DR

This paper presents a straightforward method to determine the spectrum's representation content of systems with SU(2) and SO(2,4) symmetries, applied to free planar Yang-Mills theory on S^3 and extended to N=4 super Yang-Mills.

Contribution

It introduces a simple, generalizable technique for extracting representation content from partition functions, specifically applied to Yang-Mills theories on S^3.

Findings

Derived explicit generating function for free planar Yang-Mills spectrum

Extended method to N=4 super Yang-Mills theory

Provided a new tool for analyzing conformal field theories

Abstract

We introduce a simple method to extract the representation content of the spectrum of a system with SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4) symmetry, such as conformal field theories in four dimensions. As a specific application we obtain an explicit generating function for the representation content of free planar Yang-Mills theory on S^3. The extension to N = 4 super Yang-Mills is also discussed.