One Loop Beta Functions in Topologically Massive Gravity

TL;DR

This paper computes the renormalization group flow of coupling constants in topologically massive 3D gravity, revealing fixed points and the behavior of the Chern-Simons coefficient.

Contribution

It provides the first calculation of the beta functions for all three couplings in topologically massive gravity, highlighting the fixed points and the invariance of the Chern-Simons coefficient.

Findings

The Chern-Simons coefficient  has a vanishing beta function.

Existence of both trivial and nontrivial fixed points for positive .

The flow of the cosmological and Newton's constants depends on .

Abstract

We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that \nu, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point.