Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM

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 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

References in corpus (7)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Holographic three-point functions of giant gravitons
• Matching of correlators in AdS_3/CFT_2
• Decagon at Two Loops
• Half-BPS SU(N) Correlators in N=4 SYM

Cited by in corpus (25)

• Gluon Scattering in AdS from CFT
• Ten dimensional symmetry of N=4 SYM correlators
• Towards the Virasoro-Shapiro Amplitude in AdS5xS5
• Supercharged AdS${}_3$ Holography
• The Virasoro-Shapiro amplitude in AdS${}_5\times$S${}^5$ and level splitting of 10d conformal symmetry
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• Generating functions and large-charge expansion of integrated correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
• Laplace-difference equation for integrated correlators of operators with general charges in $\mathcal{N}=4$ SYM
• One-loop string corrections for AdS Kaluza-Klein amplitudes
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Revisiting Extremal Couplings in AdS/CFT
• Charged test-particle scattering and effective one-body metrics with spin
• Integrality, Duality and Finiteness in Combinatoric Topological Strings
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• One-loop string amplitudes in AdS${}_5\times$S${}^5$: Mellin space and sphere splitting
• Scattering bound states in AdS
• On topological recursion for Wilson loops in $\mathcal{N}=4$ SYM at strong coupling
• D-branes and Orbit Average
• Four-point correlators in N=4 SYM from AdS${}_5$ bubbling geometries
• A Holographic Constraint on Scale Separation
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Precision holography of AdS${}_5$ bubbling geometries
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills