Multiple realisations of N = 1 vacua in six dimensions

Abstract

A while ago, examples of N = 1 vacua and D = 6 were constructed as orientifolds of type IIB string theory compactified on the K3 surface. Among the interesting features of those models was the presence of D5-branes behaving like small instantons, and the appearance of extra tensor multiplets. These are both non-perturbative phenomena from the point of view of heterotic string theory. Although the orientifold models are a natural setting in which to study these non-perturbative heterotic string phenomena, it is interesting and instructive to explore how such vacua are realised in heterotic string theory, M-theory and F-theory, and consider the relations between them. In particular, we consider models of M-theory compactified on K3 × S 1/ Z 2 with fivebranes present on the interval. There is a family of such models which yields the same spectra as a subfamily of the orientifold models. By further compactifying on T 2 to four dimensions we relate them to heterotic string spectra. We then use heterotic/type IIA duality to deduce the existence of Calabi-Yau 3-folds which should yield the original six-dimensional orientifold spectra if we use them to compactify F-theory. Finally, we show in detail how to take a limit of such an F-theory compactification which returns us to the type IIB orientifold models.