SUSY and Flat Direction in de Sitter Space

Abstract

We have found that supersymmetry (SUSY) in curved space is broken softly. It is also found that Pauli-Villars regularization preserves the remaining symmetry, softly broken SUSY. Using it we computed the one-loop effective potential along a (classical) flat direction in a Wess-Zumino model in de Sitter space. The analysis is relevant to the Affleck-Dine mechanism for baryogenesis. The effective potential is unbounded from below: $V_{eff}(\varphi )\to -3g^2{H}^2{\varphi }^{2}ln{\varphi }^2/16{\pi }^2$, where $\varphi$ is the scalar field along the flat direction, g is a typical coupling constant, and H is the Hubble parameter. This is identical with the effective potential which is obtained by using proper-time cutoff regularization. Since proper-time cutoff regularization is exact even at the large curvature region, the effective potential possesses softly broken SUSY and reliability in the large curvature region.

Comments: 32 pages, Latex, 14 figures. Reference added, minor changes in Discussion are made