Renormalization group equations in curved space-time with non-trivial Topology

TL;DR

This paper develops renormalization group equations for massless GUTs in curved space-time with complex topology, analyzing their behavior at different energy scales and showing the diminishing role of Casimir energy in the early Universe.

Contribution

It formulates the renormalization group equations in curved space-time with non-trivial topology and studies the effective action's asymptotics at high and low energies.

Findings

Casimir energy becomes negligible at high curvature.

Effective action asymptotics are derived for both high and low energies.

Provides a framework for understanding GUTs in complex space-time geometries.

Abstract

Renormalization group equations for massless GUT's in curved space-time with non-trivial topology are formulated. The asymptotics of the effective action both at high and low energies are obtained. It is shown that the Casimir energy contribution at high curvature (early Universe) becomes non-essential in the effective action.