Single particle operators and their correlators in free N $$ \mathcal{N} $$ = 4 SYM
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Received: August 10, 2020 Accepted: October 7, 2020 Published: November 16, 2020
Single particle operators and their correlators in free N = 4 SYM
a
Dipartimento di Fisica, Università di Milano-Bicocca, Piazza della Scienza, U2, I-20126 Milano, Italy b INFN — Sezione di Milano-Bicocca, Piazza della Scienza, U2, I-20126 Milano, Italy c School of Physics and Astronomy and STAG Research Centre, University of Southampton, Highfield, SO17 1BJ, U.K. d Mathematics Department, Durham University, Science Laboratories, South Rd, Durham DH1 3LE, U.K. e INFN — Sezione di Roma 3, Via della Vasca Navale 84, I-00146 Roma, Italy
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] 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 AdS 5 × S 5 . 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 S 3 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 twopoint function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-tomaximally 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
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)072
JHEP11(2020)072
F. Aprile,a,b J.M. Drummond,c P. Heslop,d H. Paul,c F. Sanfilippo,e M. Santagatac and A. Stewartd
expansion on the multi-particle basis which provides an alternative construction of fourand higher-point functions in the free theory. Keywords: 1/N Expansion, AdS-CFT Correspondence, Supersymmetric Gauge Theory ArXiv ePrint: 2007.09395
JHEP11(2020)072
Contents 1 Introduction
1 3 4 7 8 11 11 12 13 15 16 17
3 Multipoint orthogonality 3.1 Proof of the theorem 3.2 Near-extremal correlators vanish 3.2.1 More cases: coincident points and multi-trace splitting
18 20 21 23
4 Exact results for correlators of SPOs 4.1 Maximally-extremal correlators 4.1.1 3-point functions 4
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