Integrable spin chains and scattering amplitudes

Abstract

In this review we show that the multi-particle scattering amplitudes in N=4 SYM at large Nc and in the multi-Regge kinematics for some physical regions have the high energy behavior appearing from the contribution of the Mandelstam cuts in the complex angular momentum plane of the corresponding t-channel partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon composite states in the adjoint representation of the gauge group SU(Nc). In the leading logarithmic approximation (LLA) their contribution to the six point amplitude is in full agreement with the known two-loop result. The Hamiltonian for the Mandelstam states constructed from n gluons in LLA coincides with the local Hamiltonian of an integrable open spin chain. We construct the corresponding wave functions using the integrals of motion and the Baxter-Sklyanin approach.

Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich (ed)

References in corpus (9)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Dressing and Wrapping
• Integrability of scattering amplitudes in N=4 SUSY
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM

Cited by in corpus (19)

• Scattering amplitudes: the most perfect microscopic structures in the universe
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• BFKL approach and 2->5 MHV amplitude
• An Introduction to On-shell Recursion Relations
• Quantum mechanics of null polygonal Wilson loops
• The colour octet representation of the non-forward BFKL Green function
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• Integrability of the evolution equations for heavy-light baryon distribution amplitudes
• One loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus
• Integrability in heavy quark effective theory
• The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• On correlators of Reggeon fields and operators of Wilson lines in high energy QCD
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb{C})$ Spin Chains
• Universal transcendentality limit of BFKL eigenvalue