Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

Delius, Gustav W.; MacKay, Niall; Short, B.J.

doi:10.1016/s0370-2693(01)01275-8

Cited by 63 publications

(104 citation statements)

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“…For relevant results on classical continuum expressions -although only associated to the reflection algebra-see also [15], and for quantum analogues -for both reflection equation and twisted Yangian-see [4]. The results found are in exact correspondence with the quantum discrete expressions derived in [4].…”

Section: The Local Discrete Poisson Structuresupporting

confidence: 55%

Boundary Lax pairs from non-ultra-local Poisson algebras

Avan¹,

Doikou

2009

Journal of Mathematical Physics

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We consider non-ultra local linear Poisson algebras on a continuous line . Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or "boundary" extensions. They are parametrized by a "boundary" scalar matrix and depend in addition on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of known quadratic quantum boundary algebras. For any choice of parameters the non-ultra local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The corresponding discrete linear algebra is constructed, and the classical boundary discrete and continuum PCM models are examined as physical examples.

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Section: The Local Discrete Poisson Structuresupporting

confidence: 55%

Boundary Lax pairs from non-ultra-local Poisson algebras

Avan¹,

Doikou

2009

Journal of Mathematical Physics

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“…Generalization of our results for any A (1) n (n > 1) ATFT will be also presented in a separate publication. Finally, a similar exhaustive analysis regarding principal chiral models (partial results maybe found in [46]) will be particularly relevant especially bearing in mind the physical significance of a specific super-symmetric principal chiral model within the AdS/CFT correspondence [47,48]. Also define the fundamental weights µ k = (µ 1 k , .…”

Section: Discussionmentioning

confidence: 99%

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

Doikou¹

2008

J. High Energy Phys.

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Generic classically integrable boundary conditions for the A (1) n affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the A (1) 2 ATFT, however our results may be generalized for any A (1) n (n > 1). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the (q) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conserved quantities that depend on free boundary parameters. It also turns out that the number of local integrals of motions for SP boundary conditions is 'double' compared to those of the SNP case.

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“…vanishes only on h, so the G-symmetry is broken to H. A similar calculation for Q (1) gives 6) which vanishes neither on h nor on m. At first it was thought that this meant that nonlocal charges were not essential for integrability [98], but it was later noticed that a modified set of nonlocal charges is conserved [99], as follows.…”

Section: Boundary Remnant Of Yangian Chargesmentioning

confidence: 99%