$R^2$ Gravity in $(2+\epsilon)$--Dimensional Quantum Gravity

TL;DR

This paper investigates $R^2$ gravity in near-two-dimensional quantum gravity, performing detailed calculations of string susceptibility and confirming consistency with Liouville theory results.

Contribution

It provides a full order calculation of string susceptibility in $(2+ ext{ extepsilon})$-dimensional quantum gravity, addressing oversubtraction issues in conformal mode dynamics.

Findings

Results agree with Liouville approach in the extepsilon ightarrow 0 limit.

Addresses oversubtraction problem in conformal mode.

Provides a comprehensive calculation of string susceptibility.

Abstract

We study $R^2$ gravity in $(2+\epsilon)$--dimensional quantum gravity. Taking care of the oversubtraction problem in the conformal mode dynamics, we perform a full order calculation of string susceptibility in the $\epsilon \rightarrow 0$ limit. The result is consistent with that obtained through Liouville approach.