Tailoring Non-Compact Spin Chains

Abstract

We study three-point correlation functions of local operators in planar $\mathcal{N}=4$ SYM at weak coupling using integrability. We consider correlation functions involving two scalar BPS operators and an operator with spin, in the so called SL(2) sector. At tree level we derive the corresponding structure constant for any such operator. We also conjecture its one loop correction. To check our proposals we analyze the conformal partial wave decomposition of known four-point correlation functions of BPS operators. In perturbation theory, we extract from this decomposition sums of structure constants involving all primaries of a given spin and twist. On the other hand, in our integrable setup these sum rules are computed by summing over all solutions to the Bethe equations. A perfect match is found between the two approaches.

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References in corpus (8)

• Wave functions and correlation functions for GKP strings from integrability
• Three-loop universal structure constants in N=4 susy Yang-Mills theory
• Tailoring Three-Point Functions and Integrability IV. Theta-morphism
• Partial domain wall partition functions
• Three-Point Functions and su(1|1) Spin Chains
• The role of leading twist operators in the Regge and Lorentzian OPE limits
• χ-Systems for Correlation Functions
• A new representation for two- and three-point correlators of operators from sl(2) sector

Cited by in corpus (27)

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• Fixing the Quantum Three-Point Function
• Three-Point Functions and su(1|1) Spin Chains
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Superconformal partial waves in Grassmannian field theories
• Novel construction and the monodromy relation for three-point functions at weak coupling
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• String Bits and the Spin Vertex
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• A new representation for two- and three-point correlators of operators from sl(2) sector
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• A note on four-point correlators of half-BPS operators in N=4 SYM
• Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
• 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
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• A study of integrable form factors in massless relativistic AdS_3
• A note on three-point functions of unprotected operators
• A study of integrable form factors in massless relativistic $Ad{S}_2$