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- Title
Single particle operators and their correlators in free N = 4 SYM.
- Authors
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.
- Subjects
OPERATOR product expansions; YANG-Mills theory; CORRELATORS; SUPERSTRING theories; OPERATOR functions
- Publication
Journal of High Energy Physics, 2020, Vol 2020, Issue 11, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP11(2020)072