Fermionic Correlators from Integrability

Abstract

We study three-point functions of single-trace operators in the su(1|1) sector of planar N = 4 SYM borrowing several tools based on Integrability. In the most general configuration of operators in this sector, we have found a determinant expression for the tree-level structure constants. We then compare the predictions of the recently proposed hexagon program against all available data. We have obtained a match once additional sign factors are included when the two hexagon form-factors are assembled together to form the structure constants. In the particular case of one BPS and two non-BPS operators we managed to identify the relevant form-factors with a domain wall partition function of a certain six-vertex model. This partition function can be explicitly evaluated and factorizes at all loops. In addition, we use this result to compute the structure constants and show that at strong coupling in the so-called BMN regime, its leading order contribution has a determinant expression.

26 pages

References in corpus (15)

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• Bethe Ansatz for Quantum Strings
• Spinning Conformal Correlators
• The su(2|2) Dynamic S-Matrix
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
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• Three-Point Functions in N=4 SYM Theory at One-Loop
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Three-point functions in $\mathcal{N}=4$ SYM: the hexagon proposal at three loops
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• Scalar products in generalized models with SU(3)-symmetry
• 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 hexagon form factors

Cited by in corpus (9)

• Hexagonalization of Correlation Functions
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Handling Handles. Part II. Stratification and Data Analysis
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Hexagons and Correlators in the Fishnet Theory
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Cutting the cylinder into squares: The square form factor