One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory

Abstract

We report on a systematic study of scalar field three-point functions in planar SU(N) N=4 super Yang-Mills theory. The motivation for this work is to provide sufficient data for future conjectures on the higher-loop form of the structure constants possibly involving integrability. For this we have computed a sample of 70 structure constants at one-loop order involving primary operators of up to and including length five built entirely from scalar fields. We observe in all 17 cases occurring in our sample that the one-loop structure constant of two protected chiral primary operators and one unprotected operator is given by a simple linear function involving the anomalous scaling dimension of the latter. Moreover, a similar simple one-loop formula is proven for the three-point structure constants of the Konishi operator and two arbitrary protected or un-protected operators. It is again determined by the anomalous scaling dimensions of the operators involved.

22 pages. The paper does not reflect the possible effects due to fermion and derivative mixings for the operators starting with length 4. These corrections are presently being worked out

References in corpus (26)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The N=4 SYM Integrable Super Spin Chain
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Integrability for the Full Spectrum of Planar AdS/CFT II
• The su(2|3) Dynamic Spin Chain
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• Five loop Konishi from AdS/CFT
• Nilpotent invariants in N=4 SYM
• On correlation functions of operators dual to classical spinning string states
• Three-Point Functions in N=4 SYM Theory at One-Loop
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Structure constants of planar N =4 Yang Mills at one loop
• On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT
• Konishi operator at intermediate coupling
• The structure of n-point functions of chiral primary operators in N=4 super Yang-Mills at one-loop
• Duality between Wilson loops and gluon amplitudes
• Towards a string bit formulation of N=4 super Yang-Mills
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• Quasilocality of joining/splitting strings from coherent states

Cited by in corpus (12)

• On semiclassical computation of 3-point functions of closed string vertex operators in AdS_5 x S^5
• Two and three-point correlators of operators dual to folded string solutions at strong coupling
• Holographic Correlation Functions for Open Strings and Branes
• Large spin expansion of semiclassical 3-point correlators in AdS_5 x S^5
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• Correlation functions of magnon and spike
• Correlation function of dyonic strings
• Finite size effect on the magnon's correlation functions
• The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector
• The SO(6) Scalar Product and Three-Point Functions from Integrability
• Correlation functions of the ABJM model