Abstract
We consider a partial light-cone limit of a correlation function of the stress-tensor multiplet and identify an integrable structure emerging at one loop order of perturbation theory. It corresponds to a noncompact open spin chain with one boundary being recoil-less while the other one fully dynamical. We solve the system by means of techniques of the Baxter operator and Separation of Variables. The eigenvalues of the separated variables define rapidities of excitations propagating on the color flux tube and encode their factorizable dynamics in the presence of a dynamical boundary.
Highlights
As we know from the gauge/string correspondence [1], planar Yang-Mills theories are, string theories in a disguise
Higher point correlation functions were addressed within a framework of the so-called hexagon expansion [3], which relies on a tessellation of the two-dimensional world-sheet defining the correlation function in the dual string description in terms of certain form factors which can be found exactly from a set of axioms valid nonperturbatively
A multiple pair-wise light-cone limit of the aforementioned correlators gives access to vacuum expectation values of Wilson loops on null polygonal contours in Minkowski space-time [4]
Summary
As we know from the gauge/string correspondence [1], planar Yang-Mills theories are, string theories in a disguise. A multiple pair-wise light-cone limit of the aforementioned correlators gives access to vacuum expectation values of Wilson loops on null polygonal contours in Minkowski space-time [4] These in turn were found to be in a dual pair with scattering amplitudes [5] of properly regularized N = 4 super-Yang-Mills theory. In this paper we study a somewhat hybrid of a function, which is obtained from multi-point correlation functions by taking a partial light-cone limit The advantage of this kinematics is that it allows one to probe boundary interactions of the flux-tube attached to a dynamical rather than recoil-less “quark”. These are nothing else as the wave functions of an off-diagonal element of the monodromy matrix analyzed more than a decade ago in Ref. In spite of the fact that the rung moves in Feynman graphs had already appeared a dozen of times in the literature before, we will repeat them in the Appendix, along with a few of other ingredients, for integrity of our presentation
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