The Bethe Ansatz Equations for Reflecting Magnons

Galleas, W.

doi:10.48550/arxiv.0902.1681

Cited by 12 publications

(31 citation statements)

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“…8 This expression differs from the one given by Eq. ( 36) in [7] by the interchange j ↔ k; however, it seems to be consistent with the conventions in [26].…”

Section: All-loop Baessupporting

confidence: 65%

“…We then use the results for these subsectors to conjecture BAEs for the full SO(6) sector. Finally, we compare these one-loop BAEs with the weak-coupling limit of the all-loop BAEs [26]. We find that these two sets of results essentially agree -the only mismatch is in the exponent of the term corresponding to the "massive" node, which also occurs in the periodic case.…”

Section: Introductionmentioning

confidence: 74%

“…All-loop BAEs for the Y = 0 brane have recently been proposed in an interesting recent paper by Galleas [26]. We now wish to compare those equations with the one-loop BAEs which we have proposed for the scalar sector.…”

Section: Comparison With All-loop Baesmentioning

confidence: 92%

“…and recalling [15] x ± (−λ) = −x ∓ (λ) , (4.10) 7 We identify the variables x ± j , z − α,j and λα,j in [26] with x ± (p j ), x + (λ (α) j ) and ũ(α) j in [7], respectively. 8 This expression differs from the one given by Eq.…”

Section: All-loop Baesmentioning

confidence: 99%

“…Another aim of this work is to construct and diagonalize the corresponding commuting transfer matrix (i.e., the generating functional for the Hamiltonian and higher local conserved charges), which would provide a direct proof of the model's integrability. Moreover, we would like to compare the one-loop BAEs with the interesting all-loop BAEs which have recently been derived by Galleas [26] (see also [27]- [29]) from the all-loop bulk and boundary S-matrices.…”

Section: Introductionmentioning

confidence: 99%

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Bethe ansatz equations for open spin chains from giant gravitons

Nepomechie

2009

J. High Energy Phys.

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We investigate the open spin chain describing the scalar sector of the Y = 0 giant graviton brane at weak coupling. We provide a direct proof of integrability in the SU (2) and SU (3) sectors by constructing the transfer matrices. We determine the eigenvalues of these transfer matrices in terms of roots of the corresponding Bethe ansatz equations (BAEs). Based on these results, we propose BAEs for the full SO(6) sector. We find that, in the weak-coupling limit, the recently-proposed all-loop BAEs essentially agree with those proposed in the present work.

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“…8 This expression differs from the one given by Eq. ( 36) in [7] by the interchange j ↔ k; however, it seems to be consistent with the conventions in [26].…”

Section: All-loop Baessupporting

confidence: 65%

Section: Introductionmentioning

confidence: 74%

Section: Comparison With All-loop Baesmentioning

confidence: 92%

Section: All-loop Baesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bethe ansatz equations for open spin chains from giant gravitons

Nepomechie

2009

J. High Energy Phys.

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A note on open‐chain transfer matrices from q‐deformed su(2|2)S‐matrices

Murgan

2009

Fortschritte der Physik

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In this note, we perform Sklyanin's construction of commuting open-chain/boundary transfer matrices to the q-deformed SU (2|2) bulk S-matrix of Beisert and Koroteev and a corresponding boundary S-matrix. This also includes a corresponding commuting transfer matrix using the graded version of the q-deformed bulk S-matrix. Utilizing the crossing property for the bulk S-matrix, we argue that the transfer matrix for both graded and non-graded versions contains a crucial factor which is essential for commutativity.

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Spectral curve for open strings attached to the Y = 0 brane

Bajnok

Kim

Palla

2014

J. High Energ. Phys.

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The concept of spectral curve is generalized to open strings in AdS/CFT with integrability preserving boundary conditions. Our definition is based on the logarithms of the eigenvalues of the open monodromy matrix and makes possible to determine all the analytic, symmetry and asymptotic properties of the quasimomenta. We work out the details of the whole construction for the Y = 0 brane boundary condition. The quasimomenta of open circular strings are explicitly calculated. We use the asymptotic solutions of the Y -system and the boundary Bethe Ansatz equations to recover the spectral curve in the strong coupling scaling limit. Using the curve the quasiclassical fluctuations of some open string solutions are also studied.

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The Bethe Ansatz Equations for Reflecting Magnons

Cited by 12 publications

References 0 publications

Bethe ansatz equations for open spin chains from giant gravitons

Bethe ansatz equations for open spin chains from giant gravitons

A note on open‐chain transfer matrices from q‐deformed su(2|2)S‐matrices

Spectral curve for open strings attached to the Y = 0 brane

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