Skip to main content

Research Repository

Advanced Search

Single Particle Operators and their Correlators in Free N=4 SYM

Aprile, F; Drummond, J.M; Heslop, P; Paul, H; Sanfilippo, F; Santagata, M; Stewart, A

Single Particle Operators and their Correlators in Free N=4 SYM Thumbnail


F Aprile

J.M Drummond

H Paul

F Sanfilippo

M Santagata

A Stewart


We consider a set of half-BPS operators in N = 4 super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS5 × S5. These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. We show that single-particle U(N) operators belong to the SU(N) subspace, thus for length greater than one they are simply the SU(N) single-particle operators. Then, we point out that at large N, as the length of the operator increases, the single-particle operator naturally interpolates between the single-trace and the S3 giant graviton. At finite N, the multi-particle basis, obtained by taking products of the single-particle operators, gives a new basis for all half-BPS states, and this new basis naturally cuts off when the length of any of the single-particle operators exceeds the number of colours. From the two-point function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-to-maximally extremal free correlators, and we discuss features of the correlators when the extremality is lowered. Finally, we describe a half-BPS projection of the operator product expansion on the multi-particle basis which provides an alternative construction of four- and higher-point functions in the free theory.


Aprile, F., Drummond, J., Heslop, P., Paul, H., Sanfilippo, F., Santagata, M., & Stewart, A. (2020). Single Particle Operators and their Correlators in Free N=4 SYM. Journal of High Energy Physics, 2020(11), Article 72.

Journal Article Type Article
Acceptance Date Oct 7, 2020
Online Publication Date Nov 16, 2020
Publication Date 2020-11
Deposit Date Nov 11, 2020
Publicly Available Date Nov 26, 2020
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2020
Issue 11
Article Number 72
Related Public URLs


Published Journal Article (877 Kb)

Publisher Licence URL

Copyright Statement
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.

You might also like

Downloadable Citations