Time-dependent Solutions with Null Killing Spinor in M-theory and Superstrings

TL;DR

This paper derives general 1/2 BPS solutions in D=11 supergravity with null Killing spinors, exploring their properties and specific examples, including the linear dilaton background and flat spacetime solutions with RR or NS-NS backgrounds.

Contribution

It provides the most general supersymmetric solutions with null Killing spinors in D=11 supergravity, including new classes of solutions characterized by a single function.

Findings

Linear dilaton background is the most general supersymmetric solution without background.

Most general flat spacetime solutions in string frame with RR or NS-NS backgrounds are characterized by a single function.

Explicit examples of 1/2 BPS solutions with null Killing spinors are constructed.

Abstract

Imposing the condition that there should be a null Killing spinor with all the metrics and background field strengths being functions of the light-cone coordinates, we find general 1/2 BPS solutions in D=11 supergravity, and discuss several examples. In particular we show that the linear dilaton background is the most general supersymmetric solution without background under the additional requirement of flatness in the string frame. We also give the most general solutions for flat spacetime in the string frame with RR or NS-NS backgrounds, and they are characterized by a single function.