Seminari del Dipartimento di Matematica

Seminario del 2012

Dott. Emanuele Latini

Conformal geometry in the bulk and holography

algebra e geometria

In this talk we present a new approach,based on a machinery called tractor calculus, to study the relation between boundary CFT and bulk geometry. The main idea is to substitute in the interior Riemannian geometry with an almost Riemannian geometry that naturally produces the conformal boundary structure, We will discuss the ambient approach to tractors calculus; then, as an example, we will show how to write down Maxwell like equations within this formalism. Our main goal will be then to solve higher form Proca equation on Einstein manifold with boundary data along conformal infinity. To this aim we will first construct the exterior tractor calculus and study the cohomology of the Thomas-D operator. We will show then how to solve Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions.