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 $14leq rleq 22$, the smooth manifolds $S^1times sharp_k(S^2times S^3)$ 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.