Supergravities with positive definite potentials and AdS pp-waves

Abstract

Ten-dimensional superstring theory (or the conjectured nonperturbative Mtheory in eleven dimensions) is the most promising candidate for a consistent quantum theory of gravity capable of unifying all known forces of nature. An important question concerning these fundamental theories is how they compactify to lower dimensions and how to obtain a real four dimensional world? In this dissertation we present new avenues for M/string theory to reduce to lower dimensions as well as to four dimensions. For example, we show that by performing a generalized Kaluza-Klein IR reduction on the low-energy field theory of the heterotic string, the resulting lower dimensional theory compactifies spontaneously on S3 to give rise to (Minkowski)6 spacetime. Furthermore, a generalized reduction of M-theory on K3 à IR compacti- fies spontaneously on S2 to give rise to a (Minkowski)4 spacetime. The generalized Kaluza-Klein reduction gauges the Cremmer-Julia type global symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion by giving the higher dimensional fields an additional dependence on the circle coordinate. We apply the generalized reduction scheme to half-maximal supergravities which are obtained from the heterotic string (or the NS-NS sector of the type-II string) compactified on a (10 − D)-dimensional torus truncated to the pure supergravity multiplet. This gives rise to new gauged supergravities in diverse dimensions with supersymmetric Minkowski à sphere vacua.Since two large extra dimensions have received much attention recently, we make a detailed study of the gauged D = 6, N = (1, 1) supergravity. In particular, we show that this theory allows for a consistent sphere reduction on S2 to give rise to D = 4, N = 2 supergravity coupled to a vector multiplet which can further be truncated to N = 1 supergravity with a chiral multiplet. We also investigate pp-waves in AdS backgrounds, i.e. pp-waves as solutions of gauged supergravities with AdS vacua. These solutions generically preserve 1 4 of the supersymmetry. We demonstrate supernumerary supersymmetries for both purely gravitational pp-waves and pp-waves supported by fields strengths. These new backgrounds provide interesting novel features of the supersymmetry enhancement for the dual conformal field theory in the infinite-momentum frame