Gravitational Dressing of Renormalization Group

TL;DR

This paper investigates how gravity influences the renormalization group flow in two-dimensional quantum field theories, revealing a specific finite renormalization of the beta function linked to the gravitational current algebra's central charge.

Contribution

It demonstrates that the one-loop beta function in 2D theories is finitely renormalized by a factor related to the gravitational $SL(2,R)$ current algebra's central charge.

Findings

The one-loop beta function is modified by a factor (k+2)/(k+1).

The gravitational dressing leads to finite renormalization effects.

The central charge plays a key role in the renormalization process.

Abstract

We study the gravitational dressing of renormalizable two-dimensional field theories. Our main result is that the one-loop $\beta$-function is finitely renormalized by the factor ${k+2\over k+1}$, where $k$ is the central charge of the gravitational $SL(2, R)$ current algebra.