Three-Point Functions and su(1|1) Spin Chains

Abstract

We compute three-point functions of general operators in the su(1|1) sector of planar N = 4 SYM in the weak coupling regime, both at tree-level and one-loop. Each operator is represented by a closed spin chain Bethe state characterized by a set of momenta parameterizing the fermionic excitations. At one-loop, we calculate both the two-loop Bethe eigenstates and the relevant Feynman diagrams for the three-point functions within our setup. The final expression for the structure constants is surprisingly simple and hints at a possible form factor based approach yet to be unveiled.

36 pages

References in corpus (33)

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Cited by in corpus (21)

• One-point Functions in Defect CFT and Integrability
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Quark--anti-quark potential in N=4 SYM
• String field theory vertex from integrability
• Tailoring Non-Compact Spin Chains
• The hexagon in the mirror: the three-point function in the SoV representation
• Handling Handles. Part II. Stratification and Data Analysis
• 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
• Hexagons and Correlators in the Fishnet Theory
• String Bits and the Spin Vertex
• Three-point correlators from string amplitudes: Mixing and Regge spins
• Fermionic Correlators from Integrability
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• 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
• A study of integrable form factors in massless relativistic AdS_3
• Three-point correlation functions from pulsating strings in AdS${}_5\times S^5$
• A study of integrable form factors in massless relativistic $Ad{S}_2$