The quaternionic Heisenberg group and Heterotic String Solutions with non-constant dilaton in dimensions 7 and 5

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-Kähler spaces previously found by the authors and, moreover, to new heterotic solutions with non-constant dilaton in dimension 5. All solutions satisfy the heterotic equations of motion up to the first order of $α^{\prime}$.

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