Abstract
We consider a set of half-BPS operators in \( \mathcal{N} \) = 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.
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Aprile, F., Drummond, J.M., Heslop, P. et al. Single particle operators and their correlators in free \( \mathcal{N} \) = 4 SYM. J. High Energ. Phys. 2020, 72 (2020). https://doi.org/10.1007/JHEP11(2020)072
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DOI: https://doi.org/10.1007/JHEP11(2020)072