Dilaton Gravity Coupled to a Nonlinear Sigma Model in $2+\epsilon$ Dimensions

TL;DR

This paper investigates the quantum behavior of dilaton gravity coupled with a nonlinear sigma model in dimensions slightly above two, revealing a new fixed point structure for the dilaton coupling function.

Contribution

It introduces a new fixed point theory for the dilaton coupling in the context of nonlinear sigma models in $2+ ext{epsilon}$ dimensions.

Findings

Identification of an ultraviolet stable fixed point for the sigma model curvature.

Discovery of a saddle point fixed point for the dilaton coupling.

Extension of fixed point analysis to curved target spaces.

Abstract

Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in $2+\epsilon$ dimensions. The ultraviolet stable fixed point for the curvature of the nonlinear sigma model demands a new fixed point theory for the dilaton coupling function. The fixed point of the dilaton coupling is a saddle point similarly to the previous case of the flat target space.