Holography is the revolutionary idea that quantum gravity can be understood by studying a non-gravitational theory on a `holographic screen' in one dimension lower. It was made precise in the situation where the gravitational theory lives on an Anti-de-Sitter (AdS) background and the holographic description involves a conformal field theory (CFT) residing on the boundary of AdS. Since then, this AdS/CFT correspondence has led to major insights in fields as diverse as black hole physics, condensed matter theory, the quark-gluon plasma and quantum information theory.
The project will focus on the case where the gravity theory lives in three spacetime dimensions; the correspondence is perhaps most powerful there because of the extended symmetries of the dual two-dimensional CFT. Since the gravity theory has black hole solutions this is an excellent laboratory for studying black hole entropy and the information puzzle in a simplified setting.
Three bulk dimensions is also the context where we know the simplest concrete models of holography; in these models the bulk theory also includes massless fields with spin greater than two. They form a promising starting point for understanding holography in other backgrounds such as Minkowski or de Sitter spacetimes.
And finally, progress was made recently towards proving the AdS/CFT correspondence in three bulk dimensions using string theory. This gave insight into the huge symmetry group underlying string theory which is waiting to be explored further.
The research will take place within this broad arena, with the specific topic to be determined by the taste of the student and recent developments in the field.