From Polygon Wilson Loops to Spin Chains and Back

Abstract

Null Polygon Wilson Loops (WL) in N=4 SYM can be computed using the Operator Product Expansion in terms of a transition amplitude on top of a color flux tube (FT). That picture is valid at any value of the 't Hooft coupling. So far it has been efficiently used at weak coupling (WC) in cases where only a single particle is flowing. At any finite value of the coupling however, an infinite number of particles are flowing on top of the color FT. A major open problem in this approach was how to deal with generic multi-particle states at WC. In this paper we study the propagation of any number of FT excitations at WC. We do this by first mapping the WL into a sum of two point functions of local operators. This map allows us to translate the integrability techniques developed for the spectrum problem back to the WL. E.g., the FT Hamiltonian can be represented as a simple kernel acting on the loop. Having an explicit representation for the FT Hamiltonian allows us to treat any number of particles on an equal footing. We use it to bootstrap some simple cases where two particles are flowing, dual to N2MHV amplitudes. The FT is integrable and therefore has other (infinite set of) conserved charges. The generating function of conserved charges is constructed from the monodromy (M) matrix between sides of the polygon. We compute it for some simple examples at leading order at WC. At strong coupling (SC), these Ms were the main ingredients of the Y-system solution. To connect the WC and SC computations, we study a case where an infinite number of particles are propagating already at leading order at WC. We obtain a precise match between the WC and SC Ms. That match is the WL analogue of the well known Frolov-Tseytlin limit where the WC and SC descriptions become identical. Hopefully, putting the WC and SC descriptions on the same footing is the first step in understanding the all loop structure.

52 pages, 14 figures, the abstract in the pdf is not encrypted and is slightly more detailed

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Cited by in corpus (20)

• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• OPE for all Helicity Amplitudes
• Nonsinglet pentagons and NMHV amplitudes
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Tailoring Non-Compact Spin Chains
• Quantum mechanics of null polygonal Wilson loops
• Fixing the Quantum Three-Point Function
• A tree-level 3-point function in the su(3)-sector of planar N=4 SYM
• Bethe Ansaetze for GKP strings
• On factorization of multiparticle pentagons
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Supersymmetric quantum mechanics of the flux tube
• Descent equation for superloop and cyclicity of OPE
• An Operator Product Expansion for Form Factors II. Born level
• Asymptotic behavior of large polygonal Wilson loops in confining gauge theories