Abstract
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=2lns (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.
Highlights
The study of the energy of the excitations on a suitably chosen vacuum state is a problem which is common to very many physical theories
This vacuum may be dubbed antiferromagnetic as the prototypical example in the realm of integrable models is the antiferromagnetic vacuum state of the Heisenberg spin chain
be using the idea of converting many (Bethe) Ansatz perspective [1], spinons may appear as holes in a distribution of a large number of real Bethe roots
Summary
The study of the energy of the excitations on a suitably chosen vacuum state is a problem which is common to very many physical theories. From the BMN (ferromagnetic) vacuum [24] (no roots) we will switch on, in the Beisert-Staudacher equations, the configurations corresponding to the GKP (antiferromagnetic) vacuum and to all possible ’elementary’ excitations over the GKP vacuum; to accomplish this, we will be using the idea of converting many (Bethe) algebraic equations describing an excited state into few non-linear integral equations (NLIEs) [25, 26, 27, 12, 13] In this way, we will obtain the quantisation conditions of all the ’elementary’ excitations over the GKP vacuum and show that the structure of these equations coincides with Bethe equations of a inhomogeneous spin chain of length R = 2 ln s with two identical (purely transmitting) defects and a SU(4) symmetry in different representations (where the particle rapidities represent the inhomogeneities). In appendix E all the ABA equations are listed
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