IIB PP-Waves with Extra Supersymmetries

TL;DR

This paper classifies IIB pp-wave backgrounds with extra supersymmetries by analyzing Killing spinor equations, identifying specific forms of the metric and flux, and finding backgrounds with up to 32 Killing spinors.

Contribution

It provides a detailed classification of IIB pp-wave solutions with additional supersymmetries, including explicit forms and the number of Killing spinors.

Findings

Identified conditions for backgrounds with extra Killing spinors.

Derived explicit forms of the metric and flux for extended supersymmetries.

Found backgrounds with 18, 20, 24, and 32 Killing spinors.

Abstract

We examine Killing spinor equations of the general IIB pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a self-dual four-form \xi(x^m,x^-) in the self-dual five-form flux. Considering non-harmonic extra Killing spinors, we find that if the backgrounds admit at least one extra Killing spinor in addition to 16 standard Killing spinors, backgrounds can be reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-), modulo coordinate transformations. We examine further the cases in which the extra Killing spinors are characterized by a set of Cartan matrices. Solving Killing spinor equations, we find IIB pp-wave backgrounds which admit 18, 20, 24 and 32 Killing spinors.