Solutions to the Hull-Strominger system with torus symmetry

We construct new smooth solutions to the Hull-Strominger system, showing that the Fu-Yau solution on torus bundles over K3 surfaces can be generalized to torus bundles over K3 orbifolds. In particular, we prove that, for $13 \leq k \leq 22$and$14\leq r\leq 22$,thesmoothmanifolds$S^1\times \sharp_k(S^2\times S^3)$and$\sharp_r (S^2 \times S^4) \sharp_{r+1} (S^3 \times S^3)$, have a complex structure with trivial canonical bundle and admit a solution to the Hull-Strominger system.