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The Classical Trigonometric rMatrix for the QuantumDeformed
"... The onedimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(22). Here we investigate the quantumdeformation of the Hubbard model in the classical limit. This leads to a novel classical rmatrix of trig ..."
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The onedimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(22). Here we investigate the quantumdeformation of the Hubbard model in the classical limit. This leads to a novel classical rmatrix of trigonometric kind. We derive the corresponding oneparameter family of Lie bialgebras as a deformation of the affine gl(22) Kac–Moody superalgebra. In particular, we discuss the affine extension as well as discrete symmetries, and we scan for simpler limiting cases, such as the rational rmatrix for the undeformed Hubbard model. ∗Typeset in GoTEXLitetm ar
qdeformed supersymmetry and dynamic magnon representations,” arXiv:0704.2069 [hepth
"... It was recently noted that the dispersion relation for the magnons of planar N = 4 SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J an ..."
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Cited by 13 (2 self)
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It was recently noted that the dispersion relation for the magnons of planar N = 4 SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(22) ⋉ R 2, we derive a qdeformed superPoincaré symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed restframe representation. We comment on aspects of the coalgebra structure and some implications for the question of boostcovariance of the Smatrix. 1 1
hepth/0703068 Geometry
, 2007
"... and topology of bubble solutions from gauge theory ..."
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astolfi, forini, grignani at pg dot infn dot it and
, 2007
"... gordonws at phas dot ubc dot ca It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform lightcone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where th ..."
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gordonws at phas dot ubc dot ca It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform lightcone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform lightcone gauge parameter. The resulting finite size effects are exponentially small in the Rcharge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model. The problem of computing conformal dimensions in planar N = 4 YangMills theory has a beautiful analog as a spin chain which is thought to be integrable [1][2][3][4]. In the limit of large Rcharge J, the dynamics of the chain are greatly simplified and, in the context of integrability, can be viewed
and
, 2007
"... gordonws at phas dot ubc dot ca It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform lightcone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where th ..."
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gordonws at phas dot ubc dot ca It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform lightcone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform lightcone gauge parameter. The resulting finite size effects are exponentially small in the Rcharge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model. The problem of computing conformal dimensions in planar N = 4 YangMills theory has a beautiful analog as a spin chain which is thought to be integrable [1][2][3][4]. In the limit of large Rcharge J, the dynamics of the chain are greatly simplified and, in the context of integrability, can be viewed as magnons which propagate on an infinite line and interact with each other with a factorized Smatrix [5]. The string theory dual of
A Quantum Affine Algebra for the Deformed Hubbard Chain
"... The integrable structure of the onedimensional Hubbard model is based on Shastry’s Rmatrix and the Yangian of a centrally extended sl(22) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose Rmatrix has recently been found. This Rmatrix is of trigono ..."
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The integrable structure of the onedimensional Hubbard model is based on Shastry’s Rmatrix and the Yangian of a centrally extended sl(22) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose Rmatrix has recently been found. This Rmatrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above mentioned Yangian and to the conventional quantum affine sl(22) algebra in two special limits. ar X iv