Reflection algebra, Yangian symmetry and bound-states in AdS/CFT

MacKay, Niall; Regelskis, Vidas

doi:10.1007/jhep01(2012)134

Cited by 8 publications

(16 citation statements)

References 66 publications

(155 reference statements)

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“…Reflection matrix for the fundamental particles was found in [16] by using the boundary Lie algebra, and the reflection matrices for the 2-particle bound-states were found in [21] by using boundary Lie algebra combined with the reflection equation. These reflection matrices were shown to follow from the twisted Yangian structure [31]. In later sections we give a more elegant form this symmetry.…”

Section: The Z = 0 Giant Gravitonmentioning

confidence: 85%

“…Thus the corresponding twisted Yangian is of the Y(g, g) type and was presented in [31]. Here we will give a more elegant form of this symmetry with the help of expressions (3.15) and (3.16).…”

Section: Z = 0 Giant Gravitonmentioning

confidence: 99%

“…κ : (a, b, c, d) → (a, b, c, d) and κ : γ → γ. This notation allows us to introduce the reflected coproduct [31],…”

Section: Scattering and Reflectionmentioning

confidence: 99%

“…These coideal subalgebras depend crucially on the corresponding boundary conditions. The boundary scattering for the Y = 0 giant graviton and the Y = 0 D7-brane are identical and were shown to be governed by a twisted Yangian of type I [29,30], the boundary scattering for the Z = 0 giant graviton is governed by the twisted Yangian of type II [31], and for the D5-brane it is the achiral twisted Yangian [32]. The boundary scattering for the Z = 0 D7-brane is special as it factorizes into non-equivalent left and right factors.…”

Section: Introductionmentioning

confidence: 98%

“…We also give a more elegant form of the Yangian symmetry of the Z = 0 giant graviton found in [31]. In the second part we construct quantum affine coideal subalgebras for q-deformed models of the Z = 0 giant graviton and the left factor of the Z = 0 D7-brane.…”

Section: Introductionmentioning

confidence: 99%

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Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

Leeuw

Regelskis

2013

J. High Energ. Phys.

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Abstract:We consider the worldsheet boundary scattering and the corresponding boundary algebras for the Z = 0 giant graviton and the Z = 0 D7-brane in the AdS/CFT correspondence. We consider two approaches to the boundary scattering, the usual one governed by the (generalized) twisted Yangians and the q-deformed model of these boundaries governed by the quantum affine coideal subalgebras. We show that the q-deformed approach leads to boundary algebras that are of a more compact form than the corresponding twisted Yangians, and thus are favourable to use for explicit calculations. We obtain the q-deformed reflection matrices for both boundaries which in the q → 1 limit specialize to the ones obtained using twisted Yangians.

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Section: The Z = 0 Giant Gravitonmentioning

confidence: 85%

Section: Z = 0 Giant Gravitonmentioning

confidence: 99%

“…κ : (a, b, c, d) → (a, b, c, d) and κ : γ → γ. This notation allows us to introduce the reflected coproduct [31],…”

Section: Scattering and Reflectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

Leeuw

Regelskis

2013

J. High Energ. Phys.

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The bound state S-matrix of the deformed Hubbard chain

Leeuw

Matsumoto

Regelskis

2012

J. High Energ. Phys.

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In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended U q (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound states. The crucial ingredient in this derivation is the affine extension of the aforementioned algebra. IntroductionIntegrable systems constitute a special class of models in mathematics and physics. Their properties allow them to be solved exactly and thus they appear to be a very useful playground for studying various systems. One common feature shared by these models is that they are closely related to some underlying algebraic structures. Thus for most of the quantum integrable systems there is some sort of large and powerful symmetry hidden in the origins of it, for example a Yangian or a quantum affine algebra. A particularly interesting example is the Hubbard model.-1 -The Hubbard model, which was named after John Hubbard, is the simplest model of interacting particles on a lattice, with only two terms in the Hamiltonian, the hopping term (kinetic energy) and the Coulomb potential [1]. The model describes an ensemble of particles in a periodic potential at sufficiently low temperatures such that all the particles may be considered to be in the lowest Bloch band and also any long-range interactions between the particles are considered to be weak enough and thus are ignored. It is based on the tight-binding approximation of the superconducting systems and the motion of electrons between the atoms of a crystalline solid. Despite its apparent simplicity, it is very rich applications and generalizations describing including phase shifts and a plethora of interesting phenomena. In the case when interactions between particles on different sites of the lattice can not be neglected and are included, the model is often referred to as the Extended Hubbard model. The particles can either be fermions, as in Hubbard's original work, or bosons, and the model is then referred as either the BoseHubbard model or the boson Hubbard model that can be used to study systems such as bosonic atoms on an optical lattice (for a decent overview of various generalizations see reprint volumes [2][3][4] and also a more recent book [5]).A very specific class of models are those that share features of the one-dimensional Hubbard model and the supersymmetric t-J model [6]. The very interesting case being the Alcaraz and Bariev model [7] having an extra spin-spin interaction term in the Hamiltonian and showing some characteristics of superconductivity. This model can be viewed as a quantum deformation of the Hubbard model in much the same way as the Heisenberg XXZ model is a quantum deformation of the XXX model. This model has a specific R-matrix which can not be written as a function of the difference of two associated spectral parameters. This paradigm is related to the very interesting but at the same time complicated algebraic properties of the model.In recent years there has been renewed in...

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