On scheme dependence of gravitational dressing of renormalization group functions

TL;DR

This paper investigates how gravitational effects influence the scheme dependence of renormalization group functions in two-dimensional field theories, revealing that only the first order coefficient remains scheme independent.

Contribution

It demonstrates that in 2D theories, only the first order coefficient of the gravitationally dressed RG beta function is scheme independent, even with matter theories having one dimensionless coupling.

Findings

Only the first order coefficient of the dressed RG beta function is scheme independent.

The first two coefficients of the original beta function are scheme independent in matter theories.

Scheme dependence appears at higher orders in gravitationally dressed RG functions.

Abstract

It is shown that for 2D field theories only the first order coefficient of the gravitationally dressed RG $\beta$-function is scheme independent. This is valid even for matter theories with one dimensionless coupling, where the first two coefficients of the original $\beta$-function are scheme independent.