We compute the one-loop beta functions of the cosmological constant, Newtons 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, $ u$, has vanishing beta function. The flow of the cosmological constant and Newtons constant depends on $ u$; we study analytically the structure of the flow and its fixed points in the limits of small and large $ u$.
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