Three-point functions in $\mathcal{N}=4$ SYM: the hexagon proposal at three loops

Abstract

Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of $\mathcal{N}=4$ super-Yang-Mills, the "hexagon program". This proposal results in several remarkable predictions, including the three-point function of two protected operators with an unprotected one in the $SU(2)$ and $SL(2)$ sectors. Such predictions consist of an "asymptotic" part---similar in spirit to the asymptotic Bethe Ansatz of Beisert and Staudacher for two-point functions---as well as additional finite-size "wrapping" Lüscher-like corrections. The focus of this paper is on such wrapping corrections, which we compute at three-loops in the $SL(2)$ sector. The resulting structure constants perfectly match the ones obtained in the literature from four-point correlators of protected operators.

18 pages, 3 tables; v2: note added, ref. added, (some) misprints corrected; v3: more ref. added, more misprints corrected

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Cited by in corpus (33)

• Tessellating cushions: four-point functions in N=4 SYM
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Structure constants at wrapping order
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• From the octagon to the SFT vertex - gluing and multiple wrapping
• Hexagons and Correlators in the Fishnet Theory
• Extracting OPE coefficient of Konishi at four loops
• Positivity of hexagon perturbation theory
• Konishi OPE coefficient at the five loop order
• Classical limit of diagonal form factors and HHL correlators
• Fermionic Correlators from Integrability
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Structure constants of operators on the Wilson loop from integrability
• Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
• Field theoretical derivation of Lüscher's formula and calculation of finite volume form factors
• The property of maximal transcendentality: calculation of Feynman integrals
• On structure constants with two spinning twist-two operators
• Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
• Diagonal Form Factors and Hexagon Form Factors II. Non-BPS Light Operator
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Spinning Hexagons
• A note on three-point functions of unprotected operators
• A study of integrable form factors in massless relativistic AdS_3
• Three twist-two, two spins, two loops
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Three-Point Functions in ABJM and Bethe Ansatz
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• Finite volume form factors in integrable theories
• Some semiclassical structure constants for AdS_4 x CP^3