Quaternionic Heisenberg Group and Heterotic String Solutions with Non-Constant Dilaton in Dimensions 7 and 5

Abstract

New smooth solutions of the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton based on the quaternionic Heisenberg group are constructed. We show that through appropriate contractions the solutions found in the \({G_2}\)-heterotic case converge to the heterotic solutions on 6-dimensional inner non-Kahler spaces previously found by the authors and, moreover, to new heterotic solutions with non-constant dilatons in dimension 5. All found solutions satisfy the heterotic equations of motion up to first order of \({\alpha^{\prime}}\).