Casimir Effect for Gauge Fields in Spaces with Negative Constant Curvature

TL;DR

This paper calculates the Casimir energy for gauge fields on hyperbolic spaces, revealing a negative topological component in even dimensions, which may have cosmological implications.

Contribution

It provides explicit formulas for the Casimir energy of abelian p-form gauge fields on hyperbolic spaces using zeta-function regularization.

Findings

Topological Casimir energy component is always negative in even dimensions.

Explicit expression derived for vacuum energy of skew-symmetric tensor fields.

Potential cosmological implications discussed for negative Casimir energy.

Abstract

We consider gauge theories based on abelian $p-$forms on real compact hyperbolic spaces. Using the zeta-function regularization method and the trace tensor kernel formula, we determine explicitly an expression for the vacuum energy (Casimir energy) corresponding to skew-symmetric tensor fields. It is shown that the topological component of the Casimir energy for co-exact forms on even-dimensional spaces, associated with the trivial character, is always negative. We infer on the possible cosmological consequences of this result.