Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations in the low energy heterotic string effective theory

TL;DR

This paper demonstrates the integrable structure of symmetry-reduced bosonic string dynamics, enabling the construction of solutions like solitons and waves through a matrix spectral problem approach.

Contribution

It introduces a novel matrix spectral problem for the symmetry-reduced heterotic string effective action, facilitating solution generation methods including solitons and waves.

Findings

Developed a $(2d+n) imes (2d+n)$ matrix spectral problem

Constructed soliton generating transformations for specific backgrounds

Enabled solution generation for various field configurations

Abstract

Integrable structure of the symmetry reduced dynamics of massless bosonic sector of the heterotic string effective action is presented. For string background equations that govern in the space-time of $D$ dimensions ($D\ge 4$) the dynamics of interacting gravitational, dilaton, antisymmetric tensor and any number $n\ge 0$ of Abelian vector gauge fields, all depending only on two coordinates, we construct an \emph{equivalent} $(2 d+n)\times(2 d+n)$ matrix spectral problem ($d=D-2$). This spectral problem provides the base for the development of various solution constructing procedures (dressing transformations, integral equation methods). For the case of the absence of Abelian gauge fields, we present the soliton generating transformations of any background with interacting gravitational, dilaton and the second rank antisymmetric tensor fields. This new soliton generating procedure is available for constructing of various types of field configurations including stationary axisymmetric fields, interacting plane, cylindrical or some other types of waves and cosmological solutions.