Solutions of the quantum Yang-Baxter equation with extra nonadditive parameters

We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N = 4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an overall phase. We carry on by diagonalizing it and obtain Bethe equations for periodic states. This proves an earlier proposal for the asymptotic Bethe equations for the su(2|3) dynamic spin chain and for N = 4 SYM.

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“…2 [46]. There are three irreps which could be described by the symbols (1|2|1|0|0), (0|2|4|2|0) and (0|0|1|2|1).…”

Section: Appendix B Alternative Notation With Su(1|2) Symmetrymentioning

confidence: 99%

The su(2|2) Dynamic S-Matrix

Beisert¹

2008

Advances in Theoretical and Mathematical Physics

635

1,364

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“…It is worth to compare this construction with the one in [41]. In this reference the affinization of the R-matrix for a quantum deformation of the SU(1|2) group was considered.…”

Section: The Su (1|2) S-matrix and Crossing Transformationsmentioning

confidence: 99%

The magnon kinematics of the AdS/CFT correspondence

Gómez¹,

Hernández²

2006

J. High Energy Phys.

126

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The planar dilatation operator of N = 4 supersymmetric Yang-Mills is the hamiltonian of an integrable spin chain whose length is allowed to fluctuate. We will identify the dynamics of length fluctuations of planar N = 4 Yang-Mills with the existence of an abelian Hopf algebra Z symmetry with non-trivial co-multiplication and antipode. The intertwiner conditions for this Hopf algebra will restrict the allowed magnon irreps to those leading to the magnon dispersion relation. We will discuss magnon kinematics and crossing symmetry on the spectrum of Z. We also consider general features of the underlying Hopf algebra with Z as central Hopf subalgebra, and discuss the giant magnon semiclassical regime.

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“…We note that the Hamiltonian in Ref. [26] differs from the bulk part (24), but that they are related to each other by a canonical transformation. Nevertheless, it will be shown that this transformation does not change the Bethe-ansatz equations in the bulk.…”

Section: The Solutions Of the Graded Rementioning

confidence: 99%

A supersymmetric Uq[osp(2|2)]-extended Hubbard model with boundary fields

et al. 2001

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A strongly correlated electron system associated with the quantum superalgebra U q [osp(2|2)] is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of boundary-reflection Kmatrices leading to four kinds of possible boundary interaction terms are found. Performing the algebraic Bethe ansatz, we diagonalize the two-level transfer matrices which characterize the charge and the spin degrees of freedom, respectively. The Bethe-ansatz equations, the eigenvalues of the transfer matrices and the energy spectrum are presented explicitly. We also construct two impurities coupled to the boundaries. In the thermodynamic limit, the ground state properties and impurity effects are discussed.

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Solutions of the quantum Yang-Baxter equation with extra nonadditive parameters

Cited by 56 publications

References 21 publications

The su(2|2) Dynamic S-Matrix

The su(2|2) Dynamic S-Matrix

The magnon kinematics of the AdS/CFT correspondence

A supersymmetric Uq[osp(2|2)]-extended Hubbard model with boundary fields

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