Single particle operators and their correlators in free $$ \mathcal{N} $$ = 4 SYM
| Autor: | Alastair Stewart, M. Santagata, Paul Heslop, James M. Drummond, F. Aprile, H. Paul, F. Sanfilippo |
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| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Physics Nuclear and High Energy Physics Pure mathematics 010308 nuclear & particles physics Explicit formulae FOS: Physical sciences Superstring theory 1/N Expansion Basis (universal algebra) AdS-CFT Correspondence 1/N expansion 01 natural sciences Projection (linear algebra) Supersymmetric Gauge Theory Operator (computer programming) High Energy Physics - Theory (hep-th) Orthogonality 0103 physical sciences lcsh:QC770-798 lcsh:Nuclear and particle physics. Atomic energy. Radioactivity Operator product expansion 010306 general physics |
| Zdroj: | Journal of High Energy Physics Journal of High Energy Physics, Vol 2020, Iss 11, Pp 1-61 (2020) |
| ISSN: | 1029-8479 |
| DOI: | 10.1007/jhep11(2020)072 |
| Popis: | 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 AdS${}_5 \times S^5$. 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 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. 46 pages, appendices A,B,C,D and many illustrations |
| Databáze: | OpenAIRE |
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