Holomorphic Bisectional Curvatures, Supersymmetry Breaking, and Affleck-Dine Baryogenesis

TL;DR

This paper explores how geometric properties of Kahler manifolds in supergravity impose constraints on Affleck-Dine baryogenesis, showing that certain curvature conditions prevent baryogenesis and analyzing implications for inflationary models.

Contribution

It establishes a No-Go theorem linking holomorphic sectional curvature to baryogenesis viability and examines conditions for inflationary supersymmetry breaking within Kahler geometry.

Findings

Affleck-Dine baryogenesis is impossible if the holomorphic sectional curvature at the origin is isotropic.

Spaces with constant holomorphic sectional curvature are ruled out for baryogenesis.

Constraints on Kahler manifolds affect models of inflation and supersymmetry breaking.

Abstract

Working in $D=4, N=1$ supergravity, we utilize relations between holomorphic sectional and bisectional curvatures of Kahler manifolds to constrain Affleck-Dine baryogenesis. We show the following No-Go result: Affleck-Dine baryogenesis cannot be performed if the holomorphic sectional curvature at the origin is isotropic in tangent space; as a special case, this rules out spaces of constant holomorphic sectional curvature (defined in the above sense) and in particular maximally symmetric coset spaces. We also investigate scenarios where inflationary supersymmetry breaking is identified with the supersymmetry breaking responsible for mass splitting in the visible sector, using conditions of sequestering to constrain manifolds where inflation can be performed.