Computing Three-Point Functions for Short Operators

Abstract

We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

35 pages; v2: references added/updated, typos fixed

References in corpus (4)

• Writing CFT correlation functions as AdS scattering amplitudes
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• On String S-matrix, Bound States and TBA
• On three-point correlation functions in the gauge/gravity duality

Cited by in corpus (19)

• Spinning AdS Propagators
• The S-matrix Bootstrap I: QFT in AdS
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Proper time to the black hole singularity from thermal one-point functions
• HHL correlators, orbit averaging and form factors
• Octagons I: Combinatorics and Non-Planar Resummations
• Growing Extra Dimensions in AdS/CFT
• The hexagon in the mirror: the three-point function in the SoV representation
• Amplitudes on plane waves from ambitwistor strings
• Scattering Massive String Resonances through Field-Theory Methods
• Three-point correlators from string amplitudes: Mixing and Regge spins
• Crossing symmetry and Higher spin towers
• On the spectrum and structure constants of short operators in N=4 SYM at strong coupling
• Amplitudes Involving Massive States Using Pure Spinor Formalism
• Open-closed superstring amplitudes using vertex operators in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• Three-point functions at strong coupling in the BMN limit
• Diagonal Form Factors and Hexagon Form Factors II. Non-BPS Light Operator
• Three-point correlation functions from pulsating strings in AdS${}_5\times S^5$
• Spacetime Bananas with EOW Branes and Spins