Non-Abelian pp-waves in D=4 supergravity theories

TL;DR

This paper demonstrates that non-Abelian pp-wave solutions are 1/2 supersymmetric in various N=1 supergravity theories, including reductions from six dimensions, and extends these solutions to non-Abelian AdS pp-waves with negative cosmological constant.

Contribution

It shows the supersymmetry properties of non-Abelian pp-waves in supergravity and provides the most general solutions in certain models, including their extension to AdS backgrounds.

Findings

Non-Abelian pp-waves are 1/2 supersymmetric solutions.

The most general supersymmetric solutions are constructed from self-dual Yang-Mills and metrics.

Extension to non-Abelian AdS pp-waves preserves 1/4 supersymmetry.

Abstract

The non-Abelian plane waves, first found in flat spacetime by Coleman and subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity theories coupled to scalar and vector multiplets, including the theory of SU(2) Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this latter case they provide the most general supersymmetric solution. Passing to the Riemannian formulation of this theory we show that the most general supersymmetric solution may be constructed starting from a self-dual Yang-Mills connection on a self-dual metric and solving a Poisson equation for e^\phi. We also present the generalization of these solutions to non-Abelian AdS pp-waves which allow a negative cosmological constant and preserve 1/4 of supersymmetry.