Holographic three-point functions for short operators

Abstract

We consider holographic three-point functions for operators dual to short string states at strong coupling in N=4 super Yang-Mills. We treat the states as point-like as they come in from the boundary but as strings in the interaction region in the bulk. The interaction position is determined by saddle point, which is equivalent to conservation of the canonical momentum for the interacting particles, and leads to conservation of their conformal charges. We further show that for large dimensions the rms size of the interaction region is small compared to the radius of curvature of the AdS space, but still large compared to the string Compton wave-length. Hence, one can approximate the string vertex operators as flat-space vertex operators with a definite momentum, which depends on the conformal and R-charges of the operator. We then argue that the string vertex operator dual to a primary operator is chosen by satisfying a twisted version of Q^L=Q^R, up to spurious terms. This leads to a unique choice for a scalar vertex operator with the appropriate charges at the first massive level. We then comment on some features of the corresponding three-point functions, including the application of these results to Konishi operators.

24 pages; v2: References added, typos fixed, minor changes

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• Octagons I: Combinatorics and Non-Planar Resummations
• Correlation functions in finite temperature CFT and black hole singularities
• Fixing the Quantum Three-Point Function
• Amplitudes on plane waves from ambitwistor strings
• Computing Three-Point Functions for Short Operators
• Thermal correlation functions in CFT and factorization
• String Bits and the Spin Vertex
• Three-point correlators from string amplitudes: Mixing and Regge spins
• Harmonic Superspace from the $Ad{S}_5\times S^5$ Pure Spinor Formalism
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
• On the spectrum and structure constants of short operators in N=4 SYM at strong coupling
• Open-closed superstring amplitudes using vertex operators in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Correlators of massive string states with conserved currents
• Three-point functions at strong coupling in the BMN limit
• Half-BPS Vertex Operators of the $Ad{S}_5\times S^5$ Superstring
• Leading finite-size effects on some three-point correlators in AdS_5 x S^5
• Scaling Dimensions in AdS/QCD and the Gluon Field Strength Propagator
• Three-point correlation functions from pulsating strings in AdS${}_5\times S^5$
• Three-point functions of semiclassical string states and conserved currents in AdS_4 x CP^3
• Spacetime Bananas with EOW Branes and Spins