Renormalization-Group Improved Effective Lagrangian for Interacting Theories in Curved Spacetime

TL;DR

This paper develops a method to compute the renormalization group improved effective Lagrangian for interacting fields in curved spacetime, with explicit results for $ ext{λ} ext{ϕ}^4$ theory and discussions on curvature-induced phase transitions.

Contribution

It introduces a novel approach for calculating the RG improved effective Lagrangian in curved spacetime, including explicit second-order curvature results for $ ext{λ} ext{ϕ}^4$ theory.

Findings

Explicit second-order curvature Lagrangian for $ ext{λ} ext{ϕ}^4$ theory.

Analysis of curvature-induced phase transitions.

Discussion of challenges in gauge theories like SU(2).

Abstract

A method for finding the renormalization group (RG) improved effective Lagrangian for a massive interacting field theory in curved spacetime is presented. As a particular example, the $\lambda \varphi^4$-theory is considered and the RG improved effective Lagrangian is explicitly found up to second order in the curvature tensors. As a further application, the curvature-induced phase transitions are discussed for both the massive and the massless versions of the theory. The problems which appear when calculating the RG improved effective Lagrangian for gauge theories are discussed, taking as example the asymptotically free SU(2) gauge model.