Geometry and Physics of String Theory

The two foundations of theoretical physics are Einstein's GeneralRelativity and the Standard Model of elementary particles. It isan outstanding problem, and an exciting challenge, to understandhow these two very successful theories can be given a unifieddescription. String Theory, or M-Theory as itsometimes called, is one of the most promising candidates for sucha unified theory. Many of the recent interesting developments inString Theory, have uncovered new and deep interconnectionsbetween Geometry and Physics. The most significant example is the anti de Sitter/Conformal Field Theory correspondence (AdS/CFT). Thiscorrespondence, also known as Maldacena's conjecture, states that aparticular type of geometry (comprising anti-de Sitter space-time)encodes the same physical information as a ConformalField Theory, which describes interacting particles in a highlysymmetric regime. This duality has been applied to a wide range ofgeometrical backgrounds, which have been linked to precise quantumfield theories, thereby providing new tools for a betterunderstanding of long-standing problems on particle physics, suchas quark confinement. Another area of String Theory, wheresophisticated geometrical tools play a crucial role is that ofcompactifications. String Theory in fact naturally live in 10 or11 dimensions, and one problem is how to deal with theextra-dimensions, in addition to the four space-time oneswhich we know. One idea is then to compactify the theory,which means ascribing to the remaining compact directions the roleof an internal symmetry of the physical theory. The objectiveof my proposed research is to study the interconnectionsbetween the geometry of String Theory and its physical implications. Ipropose to investigate the AdS/CFT correspondence and itsextensions, as well the problem of String Theory compactificationswith the two-fold aim of shedding light on fundamental problems ofM-Theory and making contact with the physical World.