Fixing the Quantum Three-Point Function

Abstract

We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and long-range spin chains. This transformation can be traced back to a combination of boost operators and an inhomogeneous version of Baxter's corner transfer matrix. We reproduce the existing results for the one-loop structure constants in a simplified form and indicate how to use the method at higher loop orders. Then we evaluate the one-loop structure constants in the quasiclassical limit and compare them with the recent strong coupling computation.

53 pages, 3 figures, v2: typos corrected, v3: section 3.1 improved, small corrections, references added

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• Current operators in integrable spin chains: lessons from long range deformations
• $T\bar{T}$-deformation and long range spin chains
• A Quantum Check of AdS/dCFT
• The hexagon in the mirror: the three-point function in the SoV representation
• Three-Point Functions and su(1|1) Spin Chains
• Novel construction and the monodromy relation for three-point functions at weak coupling
• Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
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• Three-point correlators from string amplitudes: Mixing and Regge spins
• Classical Integrability for Three-point Functions: Cognate Structure at Weak and Strong Couplings
• Holographic three-point correlators in the Schrodinger/dipole CFT correspondence
• The kinematical AdS5xS5 Neumann coefficient
• Giant magnons and spiky strings in the Schrodinger/dipole-deformed CFT correspondence
• Irrelevant Deformations with Boundaries and Defects
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Diagonal Form Factors and Hexagon Form Factors II. Non-BPS Light Operator
• String theory on the Schrodinger pp-wave background
• On the Semi-Classical Limit of Scalar Products of the XXZ Spin Chain
• Three-point correlation functions from pulsating strings in AdS${}_5\times S^5$
• From Spin Vertex to String Vertex