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

TL;DR

This paper constructs new local solutions to the Hull-Strominger system on Calabi-Yau manifolds with T^3 fibrations, interpreting Hermitian Yang-Mills conditions as complex flat connections and analyzing their spectra.

Contribution

It introduces novel T^3-invariant heterotic solutions, including abelian and non-abelian examples, with corrected equations accounting for '-effects, and proposes a spectrum computation method.

Findings

Constructed new local solutions to the Hull-Strominger system.

Derived corrected equations for complex flat connections.

Proposed a spectrum computation method for non-abelian models.

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 $\alpha'$-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.