PIRSA:11110000 Scientific Series Quantum Fields and Strings

DOI10.48660/11110000

Series: Quantum Fields and Strings

Paulos, M. (2011). Mellin Amplitudes in AdS/CFT. Perimeter Institute. https://pirsa.org/11110000

Paulos, Miguel. Mellin Amplitudes in AdS/CFT. Perimeter Institute, Nov. 22, 2011, https://pirsa.org/11110000 

@misc{ pirsa_PIRSA:11110000,
  doi = {10.48660/11110000},
  url = {https://pirsa.org/11110000},
  author = {Paulos, Miguel},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Mellin Amplitudes in AdS/CFT},
  publisher = {Perimeter Institute},
  year = {2011},
  month = {nov},
  note = {PIRSA:11110000 see, \url{https://pirsa.org}}
}

Abstract

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. 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.

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