T-dual solutions of the Hull–Strominger system on non-Kähler threefolds

We construct new examples of solutions of the Hull–Strominger system on non-Kähler torus bundles over K3 surfaces, with the property that the connection <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>∇</m:mo> </m:math> {∇} on the tangent bundle is Hermite–Yang–Mills. With this ansatz for the connection <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>∇</m:mo> </m:math> {∇} , we show that the existence of solutions reduces to known results about moduli spaces of slope-stable sheaves on a K3 surface, combined with elementary analytical methods. We apply our construction to find the first examples of T-dual solutions of the Hull–Strominger system on compact non-Kähler manifolds with different topology.