Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: Scattering, particles and minimal area Wilson loops

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 = 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. *

Strong Wilson polygons from the lodge of free and bound mesons

“…In view of the one-loop corrections to the Nekrasov-Shatashvili [44] prepotential [45,46] (cf. [42] for the similarity with the present series), we shall hope that this method give the nextto-leading order (NLO); we will be glad to comment on this point in section 7, Conclusion and outlook.…”

“…Naturally, for specific tests one has to expand each term of the series 4 at either weak (see, for instance, [32,[38][39][40][41] and references therein) or strong coupling [33,34,42], and compare respectively against gauge or string theory computations. Of course there are also serious hints that this method is more efficient than both perturbative theories, and also shall give results in the unexplored intermediate region.…”

“…Already in the paper [42], we have computed the single terms and re-summed, at (LO) large coupling, the OPE for the hexagon [22], as proposed by BSV [31], but with an important modification, thanks also to our previous results on the scattering [29] over the GKP vacuum [26]. In specific, we deliberately inverted the order of collinear limit (the series) with the large coupling one in an educated manner: in fact, motivated by a pole in the fermion-antifermion S-matrix at generic coupling, we have performed a bootstrap on the (asymptotic) Bethe Anstaz equations of [42] and thus shown the existence of a new mass 2 particle in two dimensions (cf.…”

“…In specific, we deliberately inverted the order of collinear limit (the series) with the large coupling one in an educated manner: in fact, motivated by a pole in the fermion-antifermion S-matrix at generic coupling, we have performed a bootstrap on the (asymptotic) Bethe Anstaz equations of [42] and thus shown the existence of a new mass 2 particle in two dimensions (cf. the discussion below and [27,33,[47][48][49]), a meson, along with its infinite bound states, only at strong coupling.…”

“…Actually, the Bethe Ansatz equations of [42] are ideal to understand the nature of the alleged bound state, the meson, as it is represented, at generic coupling, by a string of a small fermion, a small anti-fermion and a triad of (massless) 'isospin carriers' (opportunely arranged so to give rise to an SU(4) R-symmetry singlet):…”