Renormalization Group Flows in Sigma--Models Coupled to Two--Dimensional Dynamical Gravity

TL;DR

This paper analyzes how two-dimensional dynamical gravity affects the renormalization group flows of sigma-models, revealing complex modifications to beta-functions and critical points at two-loop order.

Contribution

It provides a two-loop calculation of gravity-dressed beta-functions in sigma-models coupled to 2D gravity, showing nontrivial corrections beyond one-loop approximations.

Findings

Gravity corrections are not simple multiplicative factors.

Critical points are significantly influenced by dynamical gravity.

Results suggest complex interplay between matter fields and gravity at quantum level.

Abstract

We consider a bosonic $\s$--model coupled to two--dimensional gravity. In the semiclassical limit, $c\rightarrow -\infty$, we compute the gravity dressing of the $\b$--functions at two--loop order in the matter fields. We find that the corrections due to the presence of dynamical gravity are {\em not} expressible simply in terms of a multiplicative factor as previously obtained at the one--loop level. Our result indicates that the critical points of the theory are nontrivially influenced and modified by the induced gravity.