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

Abstract

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.

Citation

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. https://doi.org/10.1007/jhep11%282020%29072

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2020
• Issue: 11
• Article Number: 72
• DOI: https://doi.org/10.1007/jhep11%282020%29072
• Public URL: https://durham-repository.worktribe.com/output/1285921
• Related Public URLs: https://arxiv.org/abs/2007.09395