Publication details for Paul HeslopAprile, F, Drummond, J. M, 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): 72.
- Publication type: Journal Article
- ISSN/ISBN: 1029-8479
- DOI: 10.1007/JHEP11(2020)072
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
- View in another repository - may include full text
Author(s) from Durham
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.