Beta Functions of Topologically Massive Supergravity

TL;DR

This paper calculates the one-loop beta functions for key parameters in three-dimensional topologically massive supergravity, revealing that the Chern-Simons coefficient remains unchanged and analyzing the flow of other constants.

Contribution

It provides the first detailed computation of beta functions in topologically massive supergravity, highlighting the fixed point structure and the invariance of the Chern-Simons coefficient.

Findings

The Chern-Simons coefficient $ u$ has a vanishing beta function.

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

Fixed points are analyzed in the limits of small and large $ u$.

Abstract

We compute the one-loop beta functions of the cosmological constant, Newton's constant and the topological mass in topologically massive supergravity in three dimensions. We use a variant of the proper time method supplemented by a simple choice of cutoff function. We find that the dimensionless coefficient of the Chern-Simons term, $\nu$, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on $\nu$; we study analytically the structure of the flow and its fixed points in the limits of small and large $\nu$.