Integrability of scattering amplitudes in N=4 SUSY

Abstract

We argue, that the multi-particle scattering amplitudes in N=4 SUSY at large $N_c$ 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 corresponding $t$-channel partial waves. The Mandelstam cuts correspond to gluon composite states in the adjoint representation of the gauge group $SU(N_c)$. The hamiltonian for these states in the leading logarithmic approximation 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.

25 pages, no figures

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Cited by in corpus (41)

• N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution
• Towards integrability for AdS3/CFT2
• BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at N=4 SUSY
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• On Yangian Symmetry in Planar N=4 SYM
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• Quantum mechanics of null polygonal Wilson loops
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• MHV amplitude for 3->3 gluon scattering in Regge limit
• NLO Corrections to the kernel of the BKP-equations
• The colour octet representation of the non-forward BFKL Green function
• Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Effective action for the Regge processes in gravity
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• Analytic properties of high energy production amplitudes in N=4 SUSY
• Integrability of the evolution equations for heavy-light baryon distribution amplitudes
• OPE for null Wilson loops and open spin chains
• Integrable spin chains and scattering amplitudes
• Graviton emission in Einstein-Hilbert gravity
• One loop light-cone QCD, effective action for reggeized gluons and QCD RFT calculus
• Integrability in heavy quark effective theory
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• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• One-loop impact factor for the emission of two gluons
• Open Spin Chains and Complexity in the High Energy Limit
• Dual conformal invariance in the Regge limit
• The long road from Regge poles to the LHC
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
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• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb{C})$ Spin Chains
• A tale of two Regge limits