A tree-level 3-point function in the su(3)-sector of planar N=4 SYM

Abstract

We classify the 3-point functions of local gauge-invariant single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills involving at least one su(3) operator. In the case of two su(3) and one su(2) operators, the tree-level 3-point function can be expressed in terms of scalar products of su(3) Bethe vectors. Moreover, if the second level Bethe roots of one of the su(3) operators is trivial (set to infinity), this 3-point function can be written in a determinant form. Using the determinant representation, we evaluate the structure constant in the semi-classical limit, when the number of roots goes to infinity.

31 pages, 17 figures

References in corpus (9)

• On three-point correlation functions in the gauge/gravity duality
• Complete 1-loop test of AdS/CFT
• On semiclassical computation of 3-point functions of closed string vertex operators in AdS_5 x S^5
• On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT
• Wave functions and correlation functions for GKP strings from integrability
• Tailoring Three-Point Functions and Integrability IV. Theta-morphism
• Three-loop universal structure constants in N=4 susy Yang-Mills theory
• Three-point correlators of twist-2 operators in N=4 SYM at Born approximation
• Norm of Bethe Wave Function as a Determinant

Cited by in corpus (24)

• One-point Functions in Defect CFT and Integrability
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• HHL correlators, orbit averaging and form factors
• 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
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• The hexagon in the mirror: the three-point function in the SoV representation
• Fixing the Quantum Three-Point Function
• Three-Point Functions and su(1|1) Spin Chains
• Computing Three-Point Functions for Short Operators
• String Bits and the Spin Vertex
• Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models
• Three-point correlators from string amplitudes: Mixing and Regge spins
• Asymptotic Four Point Functions
• Comments on World-Sheet Form Factors in AdS/CFT
• Colour-independent partition functions in coloured vertex models
• A new representation for two- and three-point correlators of operators from sl(2) sector
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Notes on Mayer Expansions and Matrix Models
• Asymptotic behaviour of two-point functions in multi-species models
• Diagonal Form Factors and Hexagon Form Factors II. Non-BPS Light Operator
• Three-point correlation functions from pulsating strings in AdS${}_5\times S^5$
• From Spin Vertex to String Vertex
• On correlation functions in the coordinate and the algebraic Bethe ansatz