Aspects of M -theory.

Abstract

This dissertation is devoted to studying various dualities and symmetries of M-theory, as well as fundamental properties of black holes. <italic>M</italic>-theory, including its versions in unusual signatures of spacetime called <italic> M</italic>*- and <italic>M</italic>'-theories, possesses holographic dualities which relate supergravity theories to the conformal field theories (CFT) on the boundary. Here CFTs dual to probe branes at the end of (anti) de Sitter space are derived in <italic>M</italic>- and <italic>M</italic>*-theories. The near horizon geometries of 2- and 5-branes in <italic>M</italic>* and <italic> M</italic>' theories are shown to be doubly holographic. The same duality is demonstrated to exist in the pp-wave limit of <italic>M</italic>-theory. The holographic technique of derivation of important thermodynamic quantities and mass for black holes in AdS space is described which utilizes the Hamilton-Jacobi approach to dealing with the symmetries of the field configuration. The framework is applied to asymptotically AdS black hole solutions of gravity theories coupled to matter in 4, 5, 6 and 7 dimensions. The generalized holonomy approach to classifying supersymmetric solutions of supergravity theories is developed for <italic>M</italic>-theory and supergravity theories with 8 supercharges. For these theories generalized holonomy groups of all fundamental supersymmetric solutions are computed and the relation of the approach to <italic>G</italic>-structure framework is discussed. Finally, the importance of higher order integrability conditions in generalized holonomy is demonstrated and used to resolve complications arising when first order integrability does not provide complete information.