Novel construction and the monodromy relation for three-point functions at weak coupling

Abstract

In this article, we shall develop and formulate two novel viewpoints and properties concerning the three-point functions at weak coupling in the SU(2) sector of the N = 4 super Yang-Mills theory. One is a double spin-chain formulation of the spin-chain and the associated new interpretation of the operation of Wick contraction. It will be regarded as a skew symmetric pairing which acts as a projection onto a singlet in the entire SO(4) sector, instead of an inner product in the spin-chain Hilbert space. This formalism allows us to study a class of three-point functions of operators built upon more general spin-chain vacua than the special configuration discussed so far in the literature. Furthermore, this new viewpoint has the signicant advantage over the conventional method: In the usual "tailoring" operation, the Wick contraction produces inner products between off-shell Bethe states, which cannot be in general converted into simple expressions. In contrast, our procedure directly produces the so-called partial domain wall partition functions, which can be expressed as determinants. Using this property, we derive simple determinantal representation for a broader class of three-point functions. The second new property uncovered in this work is the non-trivial identity satisfied by the three-point functions with monodromy operators inserted. Generically this relation connects three-point functions of different operators and can be regarded as a kind of Schwinger-Dyson equation. In particular, this identity reduces in the semiclassical limit to the triviality of the product of local monodromies around the vertex operators, which played a crucial role in providing all important global information on the three-point function in the strong coupling regime. This structure may provide a key to the understanding of the notion of "integrability" beyond the spectral level.

35 pages;v2 Minor corrections made. An appendix and references added;v3 Typos corrected

References in corpus (13)

• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Three-point functions in the SU(2) sector at strong coupling
• Tailoring Non-Compact Spin Chains
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Wave functions and correlation functions for GKP strings from integrability
• Fixing the Quantum Three-Point Function
• 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
• String Bits and the Spin Vertex
• A new representation for two- and three-point correlators of operators from sl(2) sector
• CFT4 as SO(4,2)-invariant TFT2

Cited by in corpus (22)

• 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
• Lectures on Yangian Symmetry
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Three-point functions in $\mathcal{N}=4$ SYM: the hexagon proposal at three loops
• String field theory vertex from integrability
• Clustering and the Three-Point Function
• The hexagon in the mirror: the three-point function in the SoV representation
• Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
• String Bits and the Spin Vertex
• Crosscap States in Integrable Field Theories and Spin Chains
• Asymptotic Four Point Functions
• Fermionic Correlators from Integrability
• The kinematical AdS5xS5 Neumann coefficient
• 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
• Interactions as conformal intertwiners in 4D QFT
• From Spin Vertex to String Vertex
• Three-point correlation functions from pulsating strings in AdS${}_5\times S^5$
• Three-Point Functions in ABJM and Bethe Ansatz
• Separation of variables for higher rank integrable models: review of recent progress