General Solution of String Inspired Nonlinear Equations

TL;DR

This paper derives the general solution for coupled nonlinear equations governing the dynamics of a D-dimensional bosonic string using Lorentz harmonic variables, revealing a coset space structure.

Contribution

It provides the first explicit general solution to the nonlinear equations of D-dimensional bosonic string dynamics using harmonic variables.

Findings

Solution parametrized by Lorentz harmonic variables.

Reveals coset space structure of the solution.

Applicable to D-dimensional string models.

Abstract

We present the general solution of the system of coupled nonlinear equations describing dynamics of $D$--dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2)- dimensional spheres $S^{D-2}={SO(1,D-1) \over SO(1,1) \times SO(D-2) \semiprod K_{D-2}}.$