Non-Kaehler heterotic string solutions with non-zero fluxes and non-constant dilaton

Abstract

Conformally compact and complete smooth solutions to the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton using the first Pontrjagin form of the (-)-connection on 6-dimensional non-Kähler nilmanifold are presented. In the conformally compact case the dilaton is determined by the real slices of the elliptic Weierstrass function. The dilaton of non-compact complete solutions is given by the fundamental solution of the Laplacian on R 4. All solutions satisfy the heterotic equations of motion up to the first order of α ′. © 2014 The Author(s).