Casimir energy of confining large $N$ gauge theories

Abstract

Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S_R^3\times \mathbb{R}$ 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.

arXiv comment4 pages, 1 figure. v2: added clarifications and typo corrections, conclusions unchanged

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• Temperature-reflection I: field theory, ensembles, and interactions
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• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories