Supersymmetry of the Schrodinger and PP Wave Solutions in Einstein-Weyl Supergravities

TL;DR

This paper explores supersymmetric Schrödinger and pp-wave solutions in Einstein-Weyl supergravity, analyzing how the presence of a massive vector field affects the preservation of supersymmetry.

Contribution

It provides explicit solutions and demonstrates how the massive vector field influences supersymmetry breaking in Einstein-Weyl supergravity.

Findings

Massive vector field breaks all supersymmetry.

Solutions without the massive vector preserve 1/4 supersymmetry.

Explicit Schrödinger and pp-wave solutions are constructed.

Abstract

We obtain the Schrodinger and general pp-wave solutions with or without the massive vector in Einstein-Weyl supergravity. The vector is an auxiliary field in the off-shell supermultiplet and it acquires a kinetic term in the Weyl-squared super invariant. We study the supersymmetry of these solutions and find that turning on the massive vector has a consequence of breaking all the supersymmetry. The Schrodinger and also the pp-wave solutions with the massive vector turned off on the other hand preserve 1/4 of the supersymmetry.