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.

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

References in corpus (5)

• Dark Energy and the Accelerating Universe
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Partition function of free conformal higher spin theory
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
• T-Reflection

Cited by in corpus (4)

• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• On the Holography of Free Yang-Mills
• Temperature-reflection I: field theory, ensembles, and interactions
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories