Implications of conformal invariance in momentum space

Bzowski, Adam; McFadden, Paul; Skenderis, Kostas

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