Beta functions of topologically massive supergravity

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 also employ two different analytic continuations of AdS3 and consider harmonic expansions on the 3-sphere as well as a 3-hyperboloid, and then show that they give the same results for the beta functions. We find that the dimensionless coefficient of the Chern-Simons term, 28, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on 28; we study analytically the structure of the flow and its fixed points in the limits of small and large ?. Open Access, \ua9 2014 The Authors