The Inverse Scattering Method, Lie-Backlund Transformations and Solitons for Low-energy Effective Field Equations of 5D String Theory

TL;DR

This paper combines inverse scattering and Lie-Backlund transformations to construct and analyze solitonic solutions in 5D string theory, revealing limitations on massless solitons and generating new massive, charged configurations.

Contribution

It introduces a novel combination of inverse scattering and Lie-Backlund methods to generate and study solitons in 5D string theory, including massive solutions.

Findings

Constructed two-soliton solutions with massless and massive properties

Demonstrated the impossibility of forming massive gravitational solitons via inverse scattering alone

Generated charged, rotating solitons using Lie-Backlund transformations

Abstract

In the framework of the 5D low-energy effective field theory of the heterotic string with no vector fields excited, we combine two non-linear methods in order to construct a solitonic field configuration. We first apply the inverse scattering method on a trivial vacuum solution and obtain an stationary axisymmetric two-soliton configuration consisting of a massless gravitational field coupled to a non-trivial chargeless dilaton and to an axion field endowed with charge. The implementation of this method was done following a scheme previously proposed by Yurova. We also show that within this scheme, is not possible to get massive gravitational solitons at all. We then apply a non-linear Lie-Backlund matrix transformation of Ehlers type on this massless solution and get a massive rotating axisymmetric gravitational soliton coupled to axion and dilaton fields endowed with charges. We study as well some physical properties of the constructed massless and massive solitons and discuss on the effect of the generalized solution generating technique on the seed solution and its further generalizations.