BPS states of D=4 N=1 supersymmetry

TL;DR

This paper classifies BPS states in four-dimensional N=1 supersymmetry, analyzing their stability, geometric structure, and specific conditions in the Wess-Zumino model, including implications for anti-de Sitter supersymmetry.

Contribution

It characterizes BPS states in D=4 N=1 supersymmetry, linking their properties to Jordan algebra geometry and deriving conditions for partial supersymmetry preservation.

Findings

BPS states form a convex cone boundary linked to Jordan algebra.

Conditions for 1/4 supersymmetry preservation in the Wess-Zumino model.

No classical configurations with 3/4 supersymmetry in the Wess-Zumino model.

Abstract

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of $4\times 4$ real symmetric matrices, and we explore some implications of the associated geometry. For the Wess-Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry.