One-Loop Renormalization of a Self-Interacting Scalar Field in Nonsimply Connected Spacetimes

TL;DR

This paper investigates how finite temperature and compactified spatial dimensions affect the one-loop renormalization of a self-interacting scalar field, revealing thermal and topological contributions to physical parameters.

Contribution

It provides a detailed analysis of the renormalization process in nonsimply connected spacetimes, highlighting the impact of topology and temperature on scalar field parameters.

Findings

Mass corrections are positive due to compactification and temperature.

Coupling constant corrections are negative under these conditions.

Triviality may occur at specific temperatures or compactification radii.

Abstract

Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the compactification and finite temperature, the renormalized physical parameters of the theory (mass and coupling constant) acquire thermal and topological contributions. In the case of one compactified spatial dimension at finite temperature, we find that the corrections to the mass are positive, but those to the coupling constant are negative. We discuss the possibility of triviality, i.e. that the renormalized coupling constant goes to zero at some temperature or at some radius of the compactified spatial dimension.