Physical Scaling and Renormalization Group in Two-Dimensional Gravity

TL;DR

This paper investigates quantum gravitational effects on the renormalization group in two-dimensional gravity, revealing that matter divergences are unaffected by gravity and deriving a renormalization factor for beta functions.

Contribution

It introduces a method to define physical scale transformations using the renormalized cosmological constant in 2D gravity.

Findings

Matter one-loop divergences are unaffected by gravitational corrections.

The renormalization factor for beta functions is derived using the renormalized cosmological constant.

The approach clarifies the role of gravitational effects in the renormalization group equations.

Abstract

Quantum gravitational effects on the renormalization group equation are studied in the $(2+\epsilon)$-dimensional approach. Divergences in a matter one-loop effective action do not receive gravitational radiative corrections. The renormalization factor for beta functions recently found by Klebanov, Kogan and Polyakov is obtained by using the renormalized cosmological constant to define the physical scale transformation.