Bekenstein entropy bound for weakly-coupled field theories on a 3-sphere

TL;DR

This paper analytically calculates high temperature partition functions for large Nc gauge theories on S^1 x S^3, demonstrating that the Bekenstein entropy bound holds under various conditions, including massless and massive matter, when zero-point energies are properly included.

Contribution

It provides a detailed analytical verification that the Bekenstein entropy bound is satisfied for weakly-coupled gauge theories on a 3-sphere across different matter contents and mass regimes.

Findings

Bekenstein bound holds for massless matter when zero-point energy is included.

Adding massive matter with Casimir energy regularization still satisfies the bound.

Partition functions are computed analytically at high temperature and compared with numerical results.

Abstract

We calculate the high temperature partition functions for SU(Nc) or U(Nc) gauge theories in the deconfined phase on S^1 x S^3, with scalars, vectors, and/or fermions in an arbitrary representation, at zero 't Hooft coupling and large Nc, using analytical methods. We compare these with numerical results which are also valid in the low temperature limit and show that the Bekenstein entropy bound resulting from the partition functions for theories with any amount of massless scalar, fermionic, and/or vector matter is always satisfied when the zero-point contribution is included, while the theory is sufficiently far from a phase transition. We further consider the effect of adding massive scalar or fermionic matter and show that the Bekenstein bound is satisfied when the Casimir energy is regularized under the constraint that it vanishes in the large mass limit. These calculations can be generalized straightforwardly for the case of a different number of spatial dimensions.