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Implications of conformal invariance in momentum space

Implications of conformal invariance in momentum space
Implications of conformal invariance in momentum space
We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (`triple-K integrals'). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. We develop systematic methods for explicitly evaluating the triple-K integrals. In odd dimensions they are given in terms of elementary functions while in even dimensions the results involve dilogarithms. In some cases, the triple-K integrals diverge and subtractions are necessary and we show how such subtractions are related to conformal anomalies. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple-K integrals and how to evaluate these integrals, while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.
hep-th
1029-8479
Bzowski, Adam
fda39beb-8f6f-480a-99ba-101a54965fbe
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Bzowski, Adam
fda39beb-8f6f-480a-99ba-101a54965fbe
McFadden, Paul
4e7762ff-9b96-4516-b333-be01784fdbae
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09

Bzowski, Adam, McFadden, Paul and Skenderis, Kostas (2014) Implications of conformal invariance in momentum space. Journal of High Energy Physics, 2014 (3), [111]. (doi:10.1007/JHEP03(2014)111).

Record type: Article

Abstract

We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a novel and very effective decomposition of tensor correlators which reduces their computation to that of a number of scalar form factors. For example, the most general 3-point function of a conserved and traceless stress-energy tensor is determined by only five form factors. Dilatations and special conformal Ward identities then impose additional conditions on these form factors. The special conformal Ward identities become a set of first and second order differential equations, whose general solution is given in terms of integrals involving a product of three Bessel functions (`triple-K integrals'). All in all, the correlators are completely determined up to a number of constants, in agreement with well-known position space results. We develop systematic methods for explicitly evaluating the triple-K integrals. In odd dimensions they are given in terms of elementary functions while in even dimensions the results involve dilogarithms. In some cases, the triple-K integrals diverge and subtractions are necessary and we show how such subtractions are related to conformal anomalies. This paper contains two parts that can be read independently of each other. In the first part, we explain the method that leads to the solution for the correlators in terms of triple-K integrals and how to evaluate these integrals, while the second part contains a self-contained presentation of all results. Readers interested only in results may directly consult the second part of the paper.

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Bzowski 2014 Article Implications Of Conformal Invariance - Version of Record
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More information

Accepted/In Press date: 17 February 2014
e-pub ahead of print date: 25 March 2014
Published date: 2014
Keywords: hep-th

Identifiers

Local EPrints ID: 443007
URI: http://eprints.soton.ac.uk/id/eprint/443007
ISSN: 1029-8479
PURE UUID: 2c329cb0-36b9-4dbe-a1ef-3f688868e87b
ORCID for Kostas Skenderis: ORCID iD orcid.org/0000-0003-4509-5472

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Date deposited: 05 Aug 2020 16:35
Last modified: 26 Nov 2021 02:58

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Author: Adam Bzowski
Author: Paul McFadden

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