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

TL;DR

This paper constructs new smooth solutions to the Strominger system using the quaternionic Heisenberg group, demonstrating convergence to known solutions in lower dimensions and satisfying heterotic equations of motion at first order.

Contribution

It introduces novel heterotic string solutions with non-constant dilaton based on the quaternionic Heisenberg group, expanding the landscape of known solutions in dimensions 7 and 5.

Findings

Solutions satisfy heterotic equations of motion up to first order in α′

Solutions converge to previously known 6D non-Kähler solutions via contractions

New 5D heterotic solutions with non-constant dilaton are constructed

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-K\"ahler 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 $\alpha^{\prime}$.