On gravitational dressing of renormalization group beta-functions beyond lowest order of perturbation theory

TL;DR

This paper derives a relation between beta-function coefficients in 2D renormalizable field theories coupled to gravity, revealing a coupling-dependent ratio beyond leading order, thus advancing understanding of gravitational effects on renormalization.

Contribution

It introduces a next-leading order relation connecting beta-functions before and after gravitational coupling in 2D theories, extending previous leading-order results.

Findings

Beta-function ratios depend on coupling constants beyond leading order.

Derived a relation between beta-functions in 2D theories with gravity.

Extended the understanding of gravitational dressing effects in renormalization.

Abstract

Based on considerations in conformal gauge I derive up to nextleading order a relation between the coefficients of beta-functions in 2D renormalizable field theories before and after coupling to gravity. The result implies a coupling constant dependence of the ratio of both beta-functions beyond leading order.