The Renormalization Group and the Effective Potential in a Curved Spacetime with Torsion

TL;DR

This paper uses the renormalization group to analyze the effective potential in curved spacetime with torsion, generalizing flat space results and exploring torsion-induced phase transitions in quantum gravity.

Contribution

It introduces a method for two-loop effective potential calculations in torsionful spacetime and explicitly computes the effective potential for conformal factors in quantum gravity with torsion.

Findings

Derived a renormalization-group improved effective potential in torsionful spacetime.

Developed a method for two-loop calculations in such spacetimes.

Discussed torsion-induced phase transitions.

Abstract

The renormalization group method is employed to study the effective potential in curved spacetime with torsion. The renormalization-group improved effective potential corresponding to a massless gauge theory in such a spacetime is found and in this way a generalization of Coleman-Weinberg's approach corresponding to flat space is obtained. A method which works with the renormalization group equation for two-loop effective potential calculations in torsionful spacetime is developed. The effective potential for the conformal factor in the conformal dynamics of quantum gravity with torsion is thereby calculated explicitly. Finally, torsion-induced phase transitions are discussed.