Moving from Beisert-Staudacher equations, the complete set of Asymptotic Bethe Ansatz equations and S-matrix for the excitations over the GKP vacuum is found. The resulting model on this new vacuum is an integrable spin chain of length R = 2 ln s (s = spin) with particle rapidities as inhomogeneities, two (purely transmitting) defects and SU (4) (residual R-)symmetry. The non-trivial dynamics of N = 4 SYM appears in elaborated dressing factors of the 2D two-particle scattering factors, all depending on the 'fundamental' one between two scalar excitations. From scattering factors we determine bound states. In particular, we study the strong coupling limit, in the non-perturbative, perturbative and giant hole regimes. Eventually, from these scattering data we construct the 4D pentagon transition amplitudes (perturbative regime). In this manner, we detail the multi-particle contributions (flux tube) to the MHV gluon scattering amplitudes/Wilson loops (OPE or BSV series) and re-sum them to the Thermodynamic Bubble Ansatz. *
Previously predicted by the S-matrix bootstrap of the excitations over the GKP quantum vacuum, the appearance of a new particle at strong coupling -formed by one fermion and one anti-fermion -is here confirmed: this two-dimensional meson shows up, along with its infinite tower of bound states, while analysing the fermionic contributions to the Operator Product Expansion (collinear regime) of the Wilson null polygon loop. Moreover, its existence, free 1 and bound, turns out to be a powerful idea in re-summing all the contributions (at large coupling) for a general n-gon (n ≥ 6) to a Thermodynamic Bethe Ansatz, which is proven to be equivalent to the known one and suggests new structures for a special Y -system.
By converting the Asymptotic Bethe Ansatz (ABA) of ${\cal N}=4$ SYM into
non-linear integral equations, we find 2D scattering amplitudes of excitations
on top of the GKP vacuum. We prove that this is a suitable and powerful set-up
for the understanding and computation of the whole S-matrix. We show that all
the amplitudes depend on the fundamental scalar-scalar one.Comment: final version, 14 pages, to appear in Physics Letters
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