Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userT-dual solutions of the Hull-Strominger system on non-Kahler threefolds
159
0
0.0
(
0
)
Authors
Mario Garcia-Fernandez
Ask ChatGPT about the research
No Arabic abstract
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 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-Kahler manifolds with different topology.
rate research
Read More
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 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 studied by Friedrich and Ivanov, the resulting system of partial differential equations describes compactifications of the heterotic string to three dimensions, and is often referred to as the $G_2$-Strominger system. We study the moduli space of solutions and prove that the space of infinitesimal deformations, modulo automorphisms, is finite dimensional. We also provide a new family of solutions to this system, on $T^3$-bundles over $K3$ surfaces and for infinitely many different instanton bundles, adapting a construction of Fu-Yau and the second named author. In particular, we exhibit the first examples of $T$-dual solutions for this system of equations.
We construct balanced metrics on the family of non-Kahler Calabi-Yau threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational curves on Kahler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of $kgeq 2$ copies of $S^3times S^3$.
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 $mathbb{R}^3$ satisfying a certain co-closure condition. We give a number of abelian and non-abelian examples, and also compute the back-reaction on the geometry through the non-trivial $alpha$-corrected heterotic Bianchi identity, which includes an important correction to the equations for the complex flat connection. These are all new local solutions to the Hull-Strominger system on $T^3timesmathbb{R}^3$. We also propose a method for computing the spectrum of certain non-abelian models, in close analogy with the Morse-Witten complex of the abelian models.
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 resulting system of partial differential equations can be regarded as an analogue of the Strominger system in $7$-dimensions. We initiate the study of the moduli space of solutions and show that it is finite dimensional using elliptic operator theory. We also relate the associated geometric structures to generalized geometry.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
