Vacuum energy on orbifold factors of spheres

Details Vacuum energy on orbifold factors of spheres Vacuum energy on orbifold factors of spheres

1992-10-02

arxiv.org/abs/hep-th/9210013v1

Nucl.Phys.B395:407-432,1993

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, latex

Scientific paper

10.1016/0550-3213(93)90223-C

The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \R$\times \S^2/\Gamma$ where $\Gamma$ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when $\Gamma$ is composed of pure rotations but not otherwise. It is shown on general grounds that the same conclusion holds for all even-dimensional factored spheres and the vacuum energies are given as generalised Bernoulli functions (i.e. Todd polynomials). The relevant $\zeta$- functions are analysed in some detail and several identities are incidentally derived. The general discussion is presented in terms of finite reflection groups.

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