One-loop effective potential in Scherk-Schwarz compactifications of pure d=5 supergravities

We perform a systematic analysis of the one-loop effective potential of pure d=5 supergravities, with supersymmetry fully broken by a Scherk-Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential V${}_1$ in the full compactified theory and its counterpart V${}_{1,red}$ in the reduced theory. We confirm that V${}_1$ is finite for any N>0, in contrast to V${}_{1,red}$. We find that for broken N=8 supergravity V${}_1$ is negative definite even after accounting for the Kaluza-Klein states. We outline a program for future work where the study of a different kind of Scherk-Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results. (© 2024 Wiley‐VCH GmbH.)