Abstract
Abstract We calculate the high temperature partition functions for SU(N c ) or U(N c ) gauge theories in the deconfined phase on S 1 × S 3, with scalars, vectors, and/or fermions in an arbitrary representation, at zero ’t Hooft coupling and large N c, 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.
Highlights
Where S is the entropy, E is the total energy, and R is the effective radius of the system under consideration
We calculate the high temperature partition functions for SU(Nc) or U(Nc) gauge theories in the deconfined phase on S1 × S3, 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 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
Before presenting the calculations of the high temperature partition functions for massive scalar and fermionic matter, we provide a review of the calculations for massless scalars, fermions, and vectors to clarify how the Bekenstein bound is satisfied at all temperatures at zero ’t Hooft coupling, while the theory is in the deconfined phase
Summary
For theories formulated on S1 × Sd−1 the Bekenstein bound relates the maximum possible entropy to the total energy according to the relationship in (1.1) such that. The derivatives of L with respect to β,. In this case satisfaction of the Bekenstein bound implies that or equivalently that. Following [2, 8, 9] we derive the high temperature partition functions for theories with massless scalars, vectors, and fermions, consider theories with massive fermions and scalars. It turns out that this depends on whether the Casimir (zero-point) energy contribution is included in log Z, and, in the case of massive matter, on how it is regularized
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