$T^3$-Invariant Heterotic Hull-Strominger Solutions

Abstract

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 ${\alpha }^{\prime }$-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 $T^3\times {\mathbb{R}}^3$. 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.

35 pages