O(d+1,d+n+1)--invariant Formulation of Stationary 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.