Eur. Phys. J. C (2012) 72: 2125
https://doi.org/10.1140/epjc/s10052-012-2125-8

Regular Article - Theoretical Physics

Supersymmetry of the Schrödinger and pp-wave solutions in Einstein–Weyl supergravities

¹ Institute for Advanced Physics & Mathematics, Zhejiang University of Technology, Hangzhou, 310032, China
² Zheijiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027, China
³ Department of Physics, Beijing Normal University, Beijing, 100875, China

^* e-mail: hsliu.zju@gmail.com

Received: 4 July 2012
Published online: 21 August 2012

Abstract

We obtain the Schrödinger 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 the consequence of breaking all the supersymmetry. The Schrödinger and also the pp-wave solutions with the massive vector turned off on the other hand preserve a quarter of the supersymmetry.