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Conformal n-point functions in momentum space

Conformal n-point functions in momentum space
Conformal n-point functions in momentum space
We present a Feynman integral representation for the general momentum-space scalar n-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of n(n−3)/2 variables which play the role of momentum-space conformal cross-ratios. It involves (n−1)(n−2)/2 integrations over momenta, with the momenta running over the edges of an (n−1)-simplex. We provide the details in the simplest non-trivial case (4-point functions), and for this case we identify values of the operator and spacetime dimensions for which singularities arise leading to anomalies and beta functions, and discuss several illustrative examples from perturbative quantum field theory and holography.
1079-7114
1-8
Bzowski, Adam
89bef061-563e-4b14-ac4d-0418692e9992
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Bzowski, Adam
89bef061-563e-4b14-ac4d-0418692e9992
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09

Bzowski, Adam, McFadden, Paul and Skenderis, Kostas (2020) Conformal n-point functions in momentum space. Physical Review Letters, 124 (13), 1-8, [131602]. (doi:10.1103/PhysRevLett.124.131602).

Record type: Article

Abstract

We present a Feynman integral representation for the general momentum-space scalar n-point function in any conformal field theory. This representation solves the conformal Ward identities and features an arbitrary function of n(n−3)/2 variables which play the role of momentum-space conformal cross-ratios. It involves (n−1)(n−2)/2 integrations over momenta, with the momenta running over the edges of an (n−1)-simplex. We provide the details in the simplest non-trivial case (4-point functions), and for this case we identify values of the operator and spacetime dimensions for which singularities arise leading to anomalies and beta functions, and discuss several illustrative examples from perturbative quantum field theory and holography.

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PhysRevLett.124.131602 - Version of Record
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More information

Accepted/In Press date: 5 March 2020
Published date: 3 April 2020

Identifiers

Local EPrints ID: 438709
URI: http://eprints.soton.ac.uk/id/eprint/438709
ISSN: 1079-7114
PURE UUID: bca53bb6-504b-441b-8759-953dd057b691
ORCID for Kostas Skenderis: ORCID iD orcid.org/0000-0003-4509-5472

Catalogue record

Date deposited: 23 Mar 2020 17:30
Last modified: 26 Nov 2021 06:33

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Contributors

Author: Adam Bzowski
Author: Paul McFadden

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