Towards Feynman rules for Mellin amplitudes in AdS/CFT

By M. Paulos. 2011

215 citations recorded by the source corpus.

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 ϕ3 theory and even a 12-pt diagram in ϕ4 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/95ace41df0616fac33f087519248f69fc49788dd

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Citations in the corpus

Conformal Partial Waves: Further Mathematical Results (2011, methodology): “More recently expressions for conformal partial waves as functions of u, v have been obtained in terms of Mellin-Barnes integral representations [4,5,6,7].”
Unitarity and the holographic S-Matrix (2011, methodology): “and it can be easily computed using the diagrammatic rules from [7, 8, 9, 10].”
Spinning conformal blocks (2011, background): “Additional progress has been made at understanding the constraints of unitarity in this context [13], as well as in exploring the recently found analogy between CFT correlation functions in the Mellin representation and scattering amplitudes [14–17].”
How to succeed at holographic correlators without really trying (2017, background): “A preliminary step in this direction is setting up the Mellin formalism for operators with spin (see [42, 53] for the state of the art of this problem).”
Spinning conformal correlators (2011, methodology): “In the case of polynomial scattering amplitudes, we can use AdS/CFT to provide an explicit map from scattering amplitudes in Md+1 to CFTd correlators.”