Self-interacting scalar fields on spacetime with compact hyperbolic spatial part

TL;DR

This paper computes the one-loop effective potential for a self-interacting scalar field in a spacetime with a compact hyperbolic spatial part, revealing how topology influences phase transitions.

Contribution

It provides a closed-form expression for the one-loop effective potential using the Selberg trace formula, incorporating non-trivial topology effects.

Findings

Effective potential explicitly calculated

Topology impacts curvature-induced phase transitions

Closed-form expressions derived for both unrenormalized and renormalized potentials

Abstract

We calculate the one-loop effective potential of a self-interacting scalar field on the spacetime of the form $\reals^2\times H^2/\Gamma$. The Selberg trace formula associated with a co-compact discrete group $\Gamma$ in $PSL(2,\reals )$ (hyperbolic and elliptic elements only) is used. The closed form for the one-loop unrenormalized and renormalized effective potentials is given. The influence of non-trivial topology on curvature induced phase transitions is also discussed.