Towards the resolution of divergences in the holographic computation of extremal correlators

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 09 February 2016.The main goal of this dissertation is to construct a better understanding of the subtleties that arise in the holographic computation of extremal correlators. It is well known that these computations, in the gravitational description, su er from divergences, but the interpretation and origin of these divergences is unclear. The study starts with detailed computations of two- and three-point functions of a scalar eld minimally coupled to gravity on Euclidean AdSd space, three-point functions of two giant gravitons and one light graviton, and three-point functions of the Kaluza-Klein gravitons, using supergravity theory. Further, we also give the computation of these same correlators in the dual CFT. These involve novel techniques in the matrix model, including methods that employ Schur polynomials in the dual gauge theory analysis. By employing the usual AdS=CFT dictionary, we argue that extremal correlators are naturally related to collinear particles. There are divergences that arise in collinear amplitudes as a consequence of the fact that the particles momenta are parallel. We therefore reach the suggestive idea that the divergences in extremal correlator computations are linked to collinear divergences. Much remains to be done to really establish this connection.LG201