Dilaton Gravity in $2+\epsilon$ Dimensions

TL;DR

This paper investigates quantum dilaton gravity in 2+epsilon dimensions, addressing divergences and showing a smooth limit as epsilon approaches zero, with implications for fixed points and related models.

Contribution

It introduces a renormalized quantum dilaton gravity framework in 2+epsilon dimensions, resolving oversubtraction issues and identifying a fixed point related to CGHS models.

Findings

Divergences are computed and renormalized at one-loop order.

Mixing between Liouville and dilaton fields removes singularities.

A fixed point action related to CGHS is identified.

Abstract

Quantum theory of dilaton gravity is studied in $2+\epsilon$ dimensions. Divergences are computed and renormalized at one-loop order. The mixing between the Liouville field and the dilaton field eliminates $1/\epsilon$ singularity in the Liouville-dilaton propagator. This smooth behavior of the dilaton gravity theory in the $\epsilon \rightarrow 0$ limit solves the oversubtraction problem which afflicted the higher orders of the Einstein gravity in $2+\epsilon$ dimensions. As a nontrivial fixed point, we find a dilaton gravity action which can be transformed to a CGHS type action.