O(d+1,d+n+1)--invariant Formulation of Stationary Heterotic String Theory

TL;DR

This paper develops symmetric and invariant formulations of the stationary heterotic string theory's matter sector, enabling new solution generation methods and simplifying equations of motion through matrix potentials and group invariance.

Contribution

It introduces two novel formulations of the heterotic string theory matter sector, one symmetric in matrix potentials and another invariant under O(d+1,d+n+1), facilitating solution generation and analysis.

Findings

New solution-generating techniques based on group invariance.

Simplification of equations of motion to Laplace equation under certain ansatz.

Framework applicable to extremal solutions in heterotic string theory.

Abstract

We present a pair of symmetric formulations of the matter sector of the stationary effective action of heterotic string theory that arises after the toroidal compactification of d dimensions. The first formulation is written in terms of a pair of matrix potentials Z_1 and Z_2 which exhibits a clear symmetry between them and can be used to generate new families of solutions on the basis of either Z_1 or Z_2; the second one is an O(d+1,d+n+1)-invariant formulation which is written in terms of a matrix vector W endowed with an O(d+1,d+n+1)-invariant scalar product which linearizes the action of the O(d+1,d+n+1) symmetry group on the coset space O(d+1,d+n+1)/[O(d+1)XO(d+n+1)]; this fact opens as well a simple solution--generating technique which can be applied on the basis of known solutions. A special class of extremal solutions is indicated by asuming a simple ansatz for the matrix vector W that reduces the equation of motion to the Laplace equation for a real scalar function.