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 ≤ k ≤ 22 13 ≤ k ≤ 22 and 14≤ r≤ 22 14 ≤ r ≤ 22 , the smooth manifolds S¹× ₖ(S²× S³) S 1 × ♯ k ( S 2 × S 3 ) and ᵣ (S² × S⁴) ᵣ₊₁ (S³ × S³) ♯ r ( S 2 × S 4 ) ♯ r + 1 ( S 3 × S 3 ) , have a complex structure with trivial canonical bundle and admit a solution to the Hull–Strominger system.