Casimir energy of confining large $N$ gauge theories

TL;DR

This paper calculates the Casimir energy of large N gauge theories on a small three-sphere, finding it vanishes at infinite N, which supports predictions from temperature-reflection symmetry.

Contribution

It provides the first explicit computation of vacuum energy in confining large N gauge theories on $S^3$, confirming theoretical predictions about its vanishing.

Findings

Vacuum energy vanishes at infinite N in studied theories

Supports temperature-reflection symmetry predictions

Provides calculable results in a confining regime

Abstract

Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S^3_R \times \mathbb{R}$ have a weakly-coupled confining regime when $R$ is small compared to the strong scale. We compute the vacuum energy of a variety of confining large $N$ non-supersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the $S^3$ Casimir energy. The $N=\infty$ renormalized vacuum energy turns out to vanish in all of the large $N$ gauge theories we have examined, confirming a striking prediction of temperature-reflection symmetry.