A new twist on heterotic string compactifications

A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We show the gauge symmetry groups that arise at special points, in figures of slices of the 17-dimensional moduli space of Wilson lines and circle radii. We then study the target space realization of the duality symmetry. Although the global continuous duality symmetries of dimensionally reduced heterotic supergravity are completely broken by the structure constants of the maximally enhanced gauge groups, the low energy effective action can be written in a manifestly duality covariant form using heterotic double field theory. As a byproduct, we show that a unique deformation of the generalized diffeomorphisms accounts for both $SO(32)$ and $E_8\times E_8$ heterotic effective field theories, which can thus be considered two different backgrounds of the same double field theory even before compactification. Finally we discuss the spontaneous gauge symmetry breaking and Higgs mechanism that occurs when slightly perturbing the background fields, both from the string and the field theory perspectives.