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 $\mathcal{N}=4$ 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.

103 pages; typos corrected, references added: journal version

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Cited by in corpus (36)

• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Clustering and the Three-Point Function
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Conical Twist Fields and Null Polygonal Wilson Loops
• Hexagon POPE: effective particles and tree level resummation
• Worldsheet scattering for the GKP string
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes
• Nonperturbative enhancement of superloop at strong coupling
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Towards NMHV amplitudes at strong coupling
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• ABJM quantum spectral curve and Mellin transform
• On the scattering of gluons in the GKP string
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Green-Schwarz superstring on the lattice
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Strong Wilson polygons from the lodge of free and bound mesons
• Resummed tree heptagon
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• MHV amplitudes at strong coupling and linearized TBA equations
• Supersymmetric quantum mechanics of the flux tube
• Lattice perturbation theory for the null cusp string
• Descent equation for superloop and cyclicity of OPE
• New linearization and reweighting for simulations of string sigma-model on the lattice
• ABJM flux-tube and scattering amplitudes
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• On analytical perturbative solution of ABJM quantum spectral curve
• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• 12 loops and triple wrapping in ABJM theory from integrability
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Hexagon Bootstrap in the Double Scaling Limit