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

TL;DR

This paper derives the complete integrable model for excitations over the GKP vacuum in N=4 SYM, connecting scattering data to Wilson loops and scattering amplitudes, especially at strong coupling.

Contribution

It provides the full set of asymptotic Bethe ansatz equations and S-matrix for GKP excitations, including dressing factors and bound states, extending understanding of the flux tube dynamics.

Findings

Derived the complete integrable spin chain model for GKP vacuum

Connected scattering data to Wilson loop and scattering amplitude calculations

Analyzed strong coupling regimes and constructed pentagon transition amplitudes

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 ${\cal N}=4$ 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.