Towards Feynman rules for Mellin amplitudes
Jul, 2011Citations per year
Abstract: (arXiv)
We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in /CFT. We evaluate 5- and 6-point Mellin amplitudes in theory and even a 12-pt diagram in 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.Note:
- 41 pages, 9 figures v3: Typos corrected. JHEP version
- Conformal and W Symmetry
- Gauge-gravity correspondence
- field theory: conformal
- exchange: current
- gauge field theory: Yang-Mills
- Feynman graph
- AdS/CFT correspondence
- correlation function
- tree approximation
- spin
References(32)
Figures(9)