Towards Feynman rules for Mellin amplitudes in AdS/CFT
Laboratoire de Physique Théorique et Hautes Energies Jussieu
Tue, Oct. 04th 2011, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in $AdS$/CFT. We evaluate 5- and 6-point Mellin amplitudes in $phi^3$ theory and even a 12-pt diagram in $phi^4$ theory, enabling us to conjecture a set of Feynman rules for scalar Mellin amplitudes. The general vertices are given in terms of Lauricella generalized hypergeometric functions. We also show how to use the same combination of Mellin transform and embedding formalism for amplitudes involving fields with spin. The complicated tensor structures which usually arise can be written as certain operators acting as projectors on much simpler index structures - essentially the same ones appearing in a flat space amplitude. Using these methods we are able to evaluate a four-point current diagram with current exchange in Yang-Mills theory.