Matrix Ernst potentials for EMDA with multiple vector fields

TL;DR

This paper introduces a matrix potential framework for the Einstein-Maxwell-Dilaton-Axion system with multiple vector fields, deriving solutions and mappings relevant to supergravity and colliding wave phenomena.

Contribution

It provides a new matrix Ernst potential formulation for the system with multiple vector fields and constructs explicit solutions including a colliding waves counterpart.

Findings

Derived a concise matrix Ernst potential representation.

Constructed explicit SWIP solutions.

Presented a Kramer-Neugebauer-type map for the reduced system.

Abstract

We show that the Einstein-Maxwell-Dilaton-Axion system with multiple vector fields (bosonic sector of the D=4, N=4 supergravity) restricted to spacetimes possessing a non-null Killing vector field admits a concise representation in terms of the Ernst-type matrix valued potentials. A constructive derivation of the SWIP solutions is given and a colliding waves counterpart of the DARN-NUT solution is obtained. SU(m,m) chiral representation of the two-dimensionally reduced system is derived and the corresponding Kramer-Neugebauer-type map is presented.