Adam Bzowski
Implications of conformal invariance in momentum space
Bzowski, Adam; McFadden, Paul; Skenderis, Kostas
Authors
Paul McFadden
Kostas Skenderis
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. In odd dimensions 3-point functions are finite without renormalisation while in even dimensions non-trivial renormalisation in required. In this paper we restrict ourselves to odd dimensions. A comprehensive analysis of renormalisation will be discussed elsewhere.
Citation
Bzowski, A., McFadden, P., & Skenderis, K. (2014). Implications of conformal invariance in momentum space. Journal of High Energy Physics, 2014(03), Article 111. https://doi.org/10.1007/jhep03%282014%29111
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 17, 2014 |
Online Publication Date | Mar 25, 2014 |
Publication Date | Mar 25, 2014 |
Deposit Date | Oct 26, 2017 |
Publicly Available Date | Jun 12, 2018 |
Journal | Journal of High Energy Physics |
Print ISSN | 1126-6708 |
Electronic ISSN | 1029-8479 |
Publisher | Scuola Internazionale Superiore di Studi Avanzati (SISSA) |
Peer Reviewed | Peer Reviewed |
Volume | 2014 |
Issue | 03 |
Article Number | 111 |
DOI | https://doi.org/10.1007/jhep03%282014%29111 |
Public URL | https://durham-repository.worktribe.com/output/1345517 |
Related Public URLs | https://arxiv.org/abs/1304.7760 |
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Copyright Statement
© The Author(s) 2014 Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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