Abstract
Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanin's Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wilson loops and prove their factorized form at leading order of 't Hooft coupling for particle number-preserving transitions that were suggested earlier in a generic case.
Highlights
Let us cast the above heuristic discussion into an operator language. We will do it for the octagon at two-loop order and generalize it to an arbitrary number of GKP excitations exchanged in a given operator product expansion (OPE) channel
One realizes that while we dealt in the solution of the open spin chain with integrals defined over the upper half-plane, the transition amplitudes entering the Wilson loops are determined by the overlap integrals on the real positive half-line
In this paper we systematically studied the open spin chain emerging in the analysis of the OPE for the null polygonal Wilson loop
Summary
It was suggested that null polygonal super-Wilson loop may serve as a generating function for all scattering amplitudes in (regularized) planar maximally supersymmetric SU(N ) Yang–Mills theory. By uplifting the contour to superspace, the duality establishes the equivalence between the vacuum expectation value of the super-Wilson loop Wn in N = 4 SYM and the reduced N -particle matrix element An of the S-matrix of the theory [5,6] that is expected to hold nonperturbatively in ’t Hooft coupling a = gY2 MNc/(4π 2). The former is determined by bosonic Aααand fermionic FαA connections. The section follows a similar construction, restricted to leading order contributions in ’t Hooft coupling
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