High Energy Physics - Theory · arXiv:1106.0512 v2 · submitted 2 Jun 2011
Quantum integrability of the Alday-Arutyunov-Frolov model
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“We then show that the quantum integrability of the AAF model follows from this constraint.”
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Abstract
We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. We then show that the quantum integrability of the AAF model follows from this constraint. In the process, we also correct some missed points in earlier works.
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| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. | contribution 0.79 | 0.96 | 0.67 | asserted 1.00 |
| We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. | contribution 0.68 | 0.96 | 0.07 | asserted 1.00 |
| We then show that the quantum integrability of the AAF model follows from this constraint. | result 0.86 | 0.95 | 0.50 | asserted 1.00 |
| In the process, we also correct some missed points in earlier works. | contribution 0.88 | 0.88 | 0.02 | asserted 0.99 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99
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Cited by 1 Pith paper
Reviewed papers on Pith that cite this one. The full citation record
- TTbar deformation and the light-cone gauge hep-th · May 2019
How the literature uses it
8 arXiv papers cite this in 23 sentences
Papers citing it · 14 sentences without a confident label
Compares with it 1 paper
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For Belavin's model, we find one such exceptional solution for some particular relation between the coupling constants.[We note here, that such a condition between the coupling constants also happens in the $AAF$ model, for which the $S$-matrix factorization occurs provided constraint on the two coupling constants of the theory [ref] .]
Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models · Introduction · 0.90
Cites it as background 5 papers
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We give here only the main formulas and definitions, and refer the reader for complete technical details to the works [ref] .
Integrable theories and generalized graded Maillet algebras · Alday-Arutyunov-Frolov model: $𝔰𝔲(1|1)$ strings in uniform gauge · 0.97
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Although its various classical and quantum integrability properties have been investigated from various points of view [ref] , the main challenge still lies in the quantization of the model, due the non-ultralocal nature of the algebra of Lax operators [ref] .
The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator · Introduction · 0.81
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In this section we briefly overview the essential properties of the $AAF$ model, referring the reader to the papers [ref] for all the technical details.
On the quantization of continuous non-ultralocal integrable systems · Overview of the Alday-Arutyunov-Frolov Model · 1.00
What it cites · 34 sentences without a confident label
Contests 2 papers
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It is not difficult to see that this remarkable scheme of cancellations would have been completely ruined had we not corrected the factor of $1/2$ missed by [ref] and the overall sign difference in comparison with by [ref] , as they were paramount for the intricate fine-tuning between the interaction terms required for $S$-matrix factorization.
New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5 · S-matrix factorization · contest 0.95
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It is not difficult to see that this remarkable scheme of cancellations would have been completely ruined had we not corrected the factor of $1/2$ missed by [ref] and the overall sign difference in comparison with by [ref] , as they were paramount for the intricate fine-tuning between the interaction terms required for $S$-matrix factorization.
Bethe Ansatz in Stringy Sigma Models · S-matrix factorization · contest 0.95
Uses the method or tool of 3 papers
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Finally, we redefine the integration variable $σ⟶σ+ 2 πJ/√(λ)$ as in [ref] , neglect the constant term in ([ref]), fix $κ= √(λ)/2$, and change the Dirac matrices basis through the similarity transformation ([ref]).
Bethe Ansatz in Stringy Sigma Models · The AAF model as quantum field theory · 0.99
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Here we give another derivation, based on a general technique which, in principle, can be applied to a large class of integrable models (see, for example, [ref] ).
The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry · Two-particle scattering · 0.85
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Here we give another derivation, based on a general technique which, in principle, can be applied to a large class of integrable models (see, for example, [ref] ).
On S-Matrix factorization of the Landau-Lifshitz model · Two-particle scattering · 0.85
Compares with 4 papers
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It is important to emphasize here a significant difference in the last interacting term of our Lagrangian ([ref]) when compared to the Lagrangian (5.5) of [ref] .
New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5 · Overview of the Alday-Arutyunov-Frolov model · 0.84
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We are now in the position to obtain the full scattering amplitude: [equation] from which, by comparison with ([ref]), we read off the $S$-matrix for the scattering of two-particle, [equation] It is crucial to notice that our $S$-matrix is the inverse of the one derived by [ref] .
Bethe Ansatz in Stringy Sigma Models · Two-particle scattering · 0.91
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That being the case, it is an interesting question to quantize the AAF model in the uniform gauge and compare its spectrum with the one obtained from the free action in [ref] .
Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector · Introduction · 0.87
Cites as background 10 papers
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In this section we review the AAF model [ref] , which emerges as a result of the consistent truncation of the superstring sigma model on $AdS_5 ×S^5$ to the $𝔰𝔲(1|1)$ sector.
New Integrable System of 2dim Fermions from Strings on AdS_5 x S^5 · Overview of the Alday-Arutyunov-Frolov model · 0.99
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The AdS/CFT correspondence [ref] has provided deep insight into the intricate dynamics of both gauge and string theories, much of which can be ascribed to the uncovering of integrable structures on both sides of the duality [ref] [For a comprehensive review of the role of integrability in the context of the AdS/CFT correspondence, see [ref] .].
The Bethe-Ansatz for N=4 Super Yang-Mills · Introduction · 0.99
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The AdS/CFT correspondence [ref] has provided deep insight into the intricate dynamics of both gauge and string theories, much of which can be ascribed to the uncovering of integrable structures on both sides of the duality [ref] [For a comprehensive review of the role of integrability in the context of the AdS/CFT correspondence, see [ref] .].
The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory · Introduction · 0.99
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