Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

TL;DR

This paper demonstrates that time-dependent M-theory plane waves with extra supersymmetries are necessarily homogeneous, and explicitly constructs such solutions, analyzing their properties and the associated Killing spinors.

Contribution

It proves the necessity of homogeneity for supersymmetric time-dependent plane waves and constructs explicit examples with extra supersymmetries from Penrose limits of G"odel-like metrics.

Findings

Time-dependent plane waves with extra supersymmetries are homogeneous.

Penrose limits of G"odel metrics yield anti-Mach type plane waves.

Explicit extra Killing spinors are identified in these solutions.

Abstract

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.