String Bits and the Spin Vertex

Abstract

We initiate a novel formalism for computing correlation functions of trace operators in the planar N=4 SYM theory. The central object in our formalism is the spin vertex, which is the weak coupling analogy of the string vertex in string field theory. We construct the spin vertex explicitly for all sectors at the leading order using a set of bosonic and fermionic oscillators. We prove that the vertex has trivial monodromy, or put in other words, it is a Yangian invariant. Since the monodromy of the vertex is the product of the monodromies of the three states, the Yangian invariance of the vertex implies an infinite exact symmetry for the three-point function. We conjecture that this infinite symmetry can be lifted to any loop order.

34 pages, 6 figures, a sign correction in eq. (3.1) and appendix added

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Cited by in corpus (20)

• One-point Functions in Defect CFT and Integrability
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Lectures on Yangian Symmetry
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Three-point functions in $\mathcal{N}=4$ SYM: the hexagon proposal at three loops
• The hexagon in the mirror: the three-point function in the SoV representation
• 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
• Crosscap States in Integrable Field Theories and Spin Chains
• Classical Integrability for Three-point Functions: Cognate Structure at Weak and Strong Couplings
• Asymptotic Four Point Functions
• Operator fusion from wavefunction overlaps: Universal finite-size corrections and application to Haagerup model
• Structure constants of operators on the Wilson loop 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
• Cutting the cylinder into squares: The square form factor
• Grassmannian Integrals as Matrix Models for Non-Compact Yangian Invariants
• Interactions as conformal intertwiners in 4D QFT
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes