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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.
We construct new examples of solutions of the Hull-Strominger system on non-Kahler torus bundles over K3 surfaces, with the property that the connection $ abla$ on the tangent bundle is Hermite-Yang-Mills. With this ansatz for the connection $ abla$,
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. First
We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the $T^3$-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat connection on $mat
We consider $G_2$ structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. The r
We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric $SU(3)$ systems with Ramond-Ramond fluxes, and generalize them to higher dimensions. We show that Four