Exploring perturbative conformal field theory in Mellin space
Exploring perturbative conformal field theory in Mellin space
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function
Nizami, Amin A.
84ea4cf2-c4e9-481a-b55c-9a07c85cb851
Rudra, Arnab
84179ec9-8bdb-43df-933f-4404fe6aedf2
Sarkar, Sourav
1c47716e-e409-4ea9-bee2-fca727182814
Verma, Mritunjay
eefb3825-946d-406e-9f92-c80ba123a3bb
24 January 2017
Nizami, Amin A.
84ea4cf2-c4e9-481a-b55c-9a07c85cb851
Rudra, Arnab
84179ec9-8bdb-43df-933f-4404fe6aedf2
Sarkar, Sourav
1c47716e-e409-4ea9-bee2-fca727182814
Verma, Mritunjay
eefb3825-946d-406e-9f92-c80ba123a3bb
Nizami, Amin A., Rudra, Arnab, Sarkar, Sourav and Verma, Mritunjay
(2017)
Exploring perturbative conformal field theory in Mellin space.
JHEP, 2017, [102].
(doi:10.1007/JHEP01(2017)102).
Abstract
We explore the Mellin representation of correlation functions in conformal field theories in the weak coupling regime. We provide a complete proof for a set of Feynman rules to write the Mellin amplitude for a general tree level Feynman diagram involving only scalar operators. We find a factorised form involving beta functions associated to the propagators, similar to tree level Feynman rules in momentum space for ordinary QFTs. We also briefly consider the case where a generic scalar perturbation of the free CFT breaks conformal invariance. Mellin space still has some utility and one can consider non-conformal Mellin representations. In this context, we find that the beta function corresponding to conformal propagator uplifts to a hypergeometric function
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Accepted/In Press date: 9 January 2017
Published date: 24 January 2017
Identifiers
Local EPrints ID: 467487
URI: http://eprints.soton.ac.uk/id/eprint/467487
ISSN: 1029-8479
PURE UUID: 8d3c2714-49e5-4943-a830-ee13deb164c6
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Date deposited: 11 Jul 2022 16:43
Last modified: 16 Mar 2024 17:06
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Author:
Amin A. Nizami
Author:
Arnab Rudra
Author:
Sourav Sarkar
Author:
Mritunjay Verma
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