Abstract
We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the T3-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat connection on ℝ3 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 α′-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 T3× ℝ3. 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.
Highlights
G2 holonomy spaces with codimension-7 singularities sitting in codimension-4 orbifold loci may give a geometry on which M-theory can produce realistic models of particle physics
One tool to investigate M-theory compactifications is the duality between M-theory on a K3 surface and the E8 × E8 heterotic string on T 3 [5]. This duality is simplest in the limit of large heterotic volume, which corresponds on the M-theory side to the half-K3 limit, where the K3 surface is stretched along one direction. This duality may be adiabatically fibered over a 3D base to obtain 4D effective theories: when the G2 holonomy space of the M-theory geometry carries a coassociative K3 fibration, we expect it to be dual to the E8 × E8 heterotic string compactified on a Calabi-Yau threefold with a fibration by special Lagrangian 3-tori, known as an SYZ fibration [6]
Compact spaces of the required type for physically realistic effective theories are not yet available: on the M-theory side, no compact G2 holonomy spaces with codimension-7 singularities sitting inside orbifold loci have been constructed, and on the heterotic side, Hermitian Yang-Mills connections over compact SYZ fibrations are not well-understood
Summary
The system of equations (2.3)–(2.5) together with the heterotic Bianchi identity (2.7) and the Hermitian Yang-Mills conditions (2.8) are often referred to as the Hull-Strominger system. It is (perturbatively) accurate modulo cubic corrections in α. I=1 where λ denotes a constant size parameter This model SU(3) structure corresponds to a flat tree-level metric. Where the dagger denotes an adjoint taken with respect to the tree-level metric from (2.11) This equation can be viewed as a stability condition on the flat connection [31]. F-term flatness condition, as we will see in the subsection
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
