The Universal Geometry of Heterotic Vacua

In a recent paper, a Kahler metric was established, correct through order \alpha', for the moduli space of heterotic vacua that admit large radius limits. This required the definition of certain covariant derivatives for the heterotic structures over the moduli space. This process required, in turn, the derivation of a series of intricate identities. In this paper we geometrise these results by studying a fibration U whose fibres are heterotic vacua and whose base is the moduli space. When endowed with appropriate structures, which include a metric and connection, wonderful things happen. Disparate results are unified into a simple tensor formulation, that is intrinsically interesting. One result of this more geometrical point of view is that we are able to rederive one of the main results of a previous long and involved paper, in less than a page. Finally, we use the universal geometry to compute how the spin connection contributes to the moduli space metric in terms of the underlying manifold X.