Integrable Systems in Stringy Gravity

TL;DR

This paper demonstrates the integrability of certain four-dimensional Einstein-Maxwell-Dilaton theories using inverse scattering, revealing hidden symmetries related to string dualities and infinite-dimensional groups.

Contribution

It establishes the integrability of Einstein-Maxwell-Dilaton theories via inverse scattering and uncovers their hidden symmetry groups, including string dualities and infinite-dimensional symmetries.

Findings

Proves integrability of Einstein-Maxwell-Dilaton theories.

Identifies the hidden symmetry group as Sp(2, R).

Shows the connection to infinite-dimensional Geroch-Kinnersley-Chitre group.

Abstract

Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions are shown to be integrable by means of the inverse scattering transform method. The proof is based on the coset-space representation of the 4-dim theory in a space-time admitting a Killing vector field. Hidden symmetry group of the four-dimensional EMDA theory, unifying T and S string dualities, is shown to be Sp(2, R) acting transitively on the coset Sp(2, R)/U(2). In the case of two-parameter Abelian space-time isometry group, the hidden symmetry is the corresponding infinite-dimensional group of the Geroch-Kinnersley-Chitre type.