Aprile, F. and Drummond, J. M. and Heslop, P. and Paul, H. and Sanfilippo, F. and Santagata, M. and Stewart, A. (2020) 'Single particle operators and their correlators in free N=4 SYM.', Journal of high energy physics., 2020 (11). 072.
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.
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|Publisher Web site:||https://doi.org/10.1007/JHEP11(2020)072|
|Publisher 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.|
|Date accepted:||07 October 2020|
|Date deposited:||26 November 2020|
|Date of first online publication:||16 November 2020|
|Date first made open access:||26 November 2020|
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