SUSY and Flat Direction in de Sitter Space

TL;DR

This paper investigates how supersymmetry is softly broken in de Sitter space, computes the one-loop effective potential along a flat direction in a Wess-Zumino model, and finds it unbounded from below, relevant to baryogenesis.

Contribution

It demonstrates that SUSY in curved space is softly broken and computes the effective potential using Pauli-Villars regularization, showing its unbounded nature in de Sitter space.

Findings

Effective potential is unbounded from below.

Pauli-Villars regularization preserves softly broken SUSY.

Results are consistent with proper-time cutoff regularization.

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: $V_{eff}(\phi)\to -3g^2H^2\phi ^2 ln \phi ^2 /16\pi ^2$, where $\phi$ 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.