Chiral supergravities

Abstract

A large class of dimensional reductions of interesting ultraviolet theories do not give rise to chiral effective theories. As the Standard Model is a chiral theory this represents an obstacle for many phenomenological constructions. The aim of this thesis will be to present a series of constructions and reductions in which chiral theories are produced, with the intention that these may be used as illustrative examples of situations in which the problems associated with chirality in dimensional reductions can be avoided. We will consider the way in which a chiral theory may be generated, in the reduction of an odd-dimensional theory, by focusing on a reduction on the orbifold S1/Z2 . In doing this we will adopt the picture in which the orbifold is viewed as being a manifold with boundaries. Many of the features of these reductions will be demonstrated by analysing seven-dimensional supergravity with six-dimensional boundaries. A critical part of this discussion will center around the cancellation of anomalies which can form on these boundaries. This cancellation will be arranged by coupling certain boundary-localised matter. We will then consider the constraints that arise in allowing a consistent set of boundary-localised matter to be coupled to a given bulk system. We will illustrate this by analysing three-dimensional supergravity on a manifold with two-dimensional boundaries. We will then demonstrate how these constructions may be carried out in an alternative formalism, in which the details become more transparent. We will also explore reductions in which chirality can be preserved, by presenting the reduction of six-dimensional gauged supergravity on a sphere and monopole background. We will show that in this case a bifurcation occurs and a consistent reduction to either a chiral or a non-chiral theory may be carried out.