The Bethe ansatz approach for factorizable centrally extended S-matrices

Abstract

We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\mathbf{su}(2|2)$ symmetry. The respective $\mathbf{su}(2|2)$ $R$-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. This mapping allows us to diagonalize inhomogeneous transfer matrices whose statistical weights are given in terms of $\mathbf{su}(2|2)$ $S$-matrices by the algebraic Bethe ansatz. As a consequence of that we derive the quantization condition on the circle for the asymptotic momenta of particles scattering by the $\mathbf{su}(2|2)\otimes \mathbf{su}(2|2)$ $S$-matrix. The result for the quantization rule may be of relevance in the study of the energy spectrum of the $Ad{S}_5\times S^5$ string sigma model in the thermodynamic limit. \

22 pages, published version

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Cited by in corpus (63)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• On String S-matrix, Bound States and TBA
• String hypothesis for the AdS_5 x S^5 mirror
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Quantum Deformations of the One-Dimensional Hubbard Model
• N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• The S-matrix of String Bound States
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Integrability of the AdS_5 x S^5 superstring and its deformations
• The Bound State S-Matrix for AdS5 x S5 Superstring
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• The spectral problem for strings on twisted AdS_5 x S^5
• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• Quantum integrability and functional equations
• Temperature quantization from the TBA equations
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Twisted Bethe equations from a twisted S-matrix
• Yangians, S-matrices and AdS/CFT
• A Yangian Double for the AdS/CFT Classical r-matrix
• Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM
• Exact S-matrices for AdS_3/CFT_2
• Lectures on S-matrices and Integrability
• Yangian of AdS3/CFT2 and its deformation
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons
• The Bethe Ansatz Equations for Reflecting Magnons
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• The Bound State S-matrix of the Deformed Hubbard Chain
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• Structure of the string R-matrix
• Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
• Bethe ansatz equations for open spin chains from giant gravitons
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Toy models for wrapping effects
• Algebraic Bethe Ansatz for U(1) Invariant Integrable Models: The Method and General Results
• Hubbard-Shastry lattice models
• The Bethe Ansatz for AdS5 x S5 Bound States
• On the $Ad{S}_5/CF{T}_4$ TBA and its analytic properties
• An alternative S-matrix for N=6 Chern-Simons theory ?
• Maximally extended sl(2|2) as a quantum double
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix
• On the origin of the dressing phase in N=4 Super Yang-Mills
• Nonlocal Symmetries and Factorized Scattering
• Fusion for the one-dimensional Hubbard model
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• An algebraic approach to the Hubbard model
• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator
• The Ising model and planar N=4 Yang-Mills
• Microscopic formulation of the S-matrix in AdS/CFT
• Bethe Ansatz for Quantum-Deformed Strings
• A range three elliptic deformation of the Hubbard model
• An Elliptic Parameterisation of the Zamolodchikov Model
• New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions
• Algebraic Geometry methods associated to the one-dimensional Hubbard model
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Multiplicity in Supersymmetric Spin Chains
• Transfer matrices for AdS3/CFT2
• A boundary matrix for AdS/CFT SU(1|1) spin chain
• Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain