New progress in the stationary D=N=4 supergravity

TL;DR

This paper introduces a new matrix representation and symmetry analysis for stationary four-dimensional supergravity, enabling advanced solution generation techniques in string theory models.

Contribution

It develops a novel 4x4 unitary null-curvature matrix representation and a new Ernst type matrix potential for stationary supergravity, expanding the mathematical framework.

Findings

Derived a new matrix representation for the theory.

Classified the hidden symmetry group and its subgroups.

Analyzed solution generation via symmetry transformations.

Abstract

A bosonic sector of the four-dimensional low-energy heterotic string theory with two Abelian gauge fields is considered in the stationary case. A new 4X4 unitary null-curvature matrix representation of the theory is derived and the corresponding formulation based on the use of a new 2X2 Ernst type matrix complex potential is developed. The group of hidden symmetries is described and classified in the matrix-valued quasi General Relativity form. A subgroup of charging symmetries is constructed and representation which transforms linearly under the action of this symmetry subgroup is established. Also the solution generation procedure based on the application of the total charging symmetry subgroup to the stationary Einstein-Maxwell theory is analyzed.