M-Theory Solutions and Intersecting D-Brane Systems

Abstract

It is believed that fundamental M-theory in the low-energy limit can be described effectively by D=11 supergravity. Extending our understanding of the different classical brane solutions in M-theory (or string theory) is important, and so there is a lot of interest in finding D=11 M-brane solutions such that after reduction to ten dimensions, they (or some combinations of them) reduce simply to the supersymmetric BPS saturated p-brane solutions. In this thesis, we study and construct M2 and M5-branes solutions in D=11 supergravity. The M-brane solutions are constructed by lifting a D-brane to a four or higher dimensional geometry embedded in M-theory and then placing M-brane solutions in the background geometry. We present new analytic M2 and M5-brane solutions in M-theory based on transverse Gibbons-Hawking and Bianchi spaces. These solutions provide realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections. One novel feature of these solutions is that the metric functions depend on more than two transverse coordinates, unlike all the other previous known solutions. Moreover since the metric functions in the Gibbons-Hawking geometries depends on more than one physical parameters, their embedding into M-theory yield new M-brane solutions with the M-brane metric functions depend on both compact and non-compact coordinates. We show that all new solutions have eight preserved supersymmetries. Upon reduction to 10 dimensions, we find that the world-volume theories of the NS5-branes decouple from the bulk for these solutions.