Special Hermitian structures and heterotic string compactifications
In this talk we will focus on the heterotic string equations with non-zero fluxes in six dimensions. Solutions to these equations have an SU(3)-structure for which the underlying almost complex structure is integrable, the holonomy of the associated Bismut connection reduces to SU(3) and the Lee form is a multiple of the differential of the dilaton function, that is, the Hermitian structure is conformally balanced. We will show general results on the balanced Hermitian geometry of 6-dimensional nilmanifolds, which lead to explicit compact solutions with non-zero field strength, non-flat instanton and constant dilaton of the heterotic string equations. This is a joint work with M. Fern‡ndez, S. Ivanov and R. Villacampa.