One‐Loop Effective Potential in Scherk–Schwarz Compactifications of Pure d=5$d=5$ Supergravities

Abstract

AbstractWe perform a systematic analysis of the one‐loop effective potential of pure 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 in the full compactified theory and its counterpart in the reduced theory. We confirm that is finite for any , in contrast to . We find that for broken supergravity 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.