Triangle Seminars

Abstract:
In the supergravity approximation of the AdS/CFT correspondence correlation fucntions of the strongly coupled gauge theory can be computed by evaluating the on-shell supergravity action with arbitrary Dirichlet boundary conditions for the various fields. It is well
known, however, that the on-shell action on the conformal boundary of AdS diverges due to the infinite volume of the bulk. Holographic Renormalization is a method for systematically constructing covariant counter terms which remove the divergences of the on-shell supergravity action for any asymptotically AdS space and it provides an algorithm for calculating renormalized correlation functions of the strongly coupled gauge theory. I will review the main steps involved in this algorithm and present a recently developed Hamiltonian version of the method where the AdS radius plays the role of time in the Hamiltonian formalism. I will then apply this method to calculate correlation functions in the field theory duals of various Poincare and AdS-sliced domain wall solutions of five dimensional gauged supergravity, including the recently discovered Janus background.

Abstract:
We will generalize the concept of partial and complete observables, intruduced by Rovelli, to constrained systems with an arbitrary number of (first class) constraints and to canonical field theories. Different methods to calculate complete observables (aka Dirac observables) will be presented and applied to examples, moreover their algebraic properties will be considered. Furthermore we will investigate whether it is possible to calculate complete observables in stages. In the case of gravity this will answer the question , whether it is possible to calculate the complete observable with respect to the Hamiltonian constraints, starting from 3-diffeomorphism invariant partial observables.