Boost generator in AdS3 integrable superstrings for general braiding

García, Juan Miguel Nieto; Торриелли, Алессандро; Wyss, Leander

doi:10.1007/jhep07(2020)223

Cited by 6 publications

(4 citation statements)

References 85 publications

(142 reference statements)

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“…More generally given some bialgebra A we require that ∆ op (a)R(u, v) = R(u, v)∆(a) where ∆ and ∆ op denote the coproduct and opposite coproduct related by conjugation on A, respectively. In many cases this is enough to completely fix R up to a small number of functions, drastically simplifying the construction, as was demonstrated in the case of AdS/CFT integrable systems [15][16][17][18][19][20][21][22], see also [23] for recent developments using this approach. Of course, this approach first requires one to know what the corresponding symmetry is and there are R-matrices which may have no such symmetry at all.…”

Section: Introductionmentioning

confidence: 99%

Yang-Baxter and the Boost: splitting the difference

et al. 2021

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In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

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Section: Introductionmentioning

confidence: 99%

Yang-Baxter and the Boost: splitting the difference

et al. 2021

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“…More generally given some bialgebra A we require that ∆ op (a)R(u, v) = R(u, v)∆(a) where ∆ and ∆ op denote the coproduct and opposite coproduct on A, respectively, cf the general discussion in section (3). In many cases this is enough to completely fix R up to a small number of functions, drastically simplifying the construction, as was demonstrated in the case of AdS/CFT integrable systems [19,[199][200][201][202][203][204][205]. Of course, this approach first requires one to know what the corresponding symmetry is and there are R-matrices which may have no such symmetry at all.…”

Section: Local Charges and Boost Automorphismmentioning

confidence: 99%

Integrable systems, separation of variables and the Yang-Baxter equation

Ryan¹

2022

Preprint

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This article, based on the author's PhD thesis, reviews recent advancements in the field of quantum integrability, in particular the separation of variables (SoV) program for high-rank integrable spin chains and the boost mechanism for solving the Yang-Baxter equation. We begin with a general overview of quantum integrable systems with special emphasis on their description in terms of quantum algebras. We then provide a detailed account of the Yangian Y(gl(n)) of gl(n) in particular the Bethe algebra, fusion and T-and Q-systems. We then introduce the notion of separation of variables in integrable systems and build on Sklyanin's work in rank 1 models and extend to higher rank. By exploiting a novel link between SoV and quantum algebra representation theory we construct the separated variables for high-rank gl(n) bosonic spin chains for arbitrary compact representations of the symmetry algebra and develop various new tools along the way. Next, we build on the previous part and develop a new technique for the computation of scalar products in the SoV framework which we call Functional SoV or FSoV. Unlike the work in the previous part, which was operatorial, this approach is functional and is based on the Baxter TQ equations. After developing this technique we supplement it with a new operator construction providing a unified view of functional and operatorial SoV. Then, we generalise the results of the previous part from compact spin chains to non-compact spin chains.The final part of this work is based on the development of tools for solving the Yang-Baxter equation. We develop a bottom-up approach for this based on the so-called Boost automorphism and uses the spin chain Hamiltonian as a starting point. Our approach allows us to classify numerous families of solutions in particular a complete classification of 4 × 4 solutions which preserve fermion number which have applications in the AdS/CFT correspondence.

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“…We believe that it must be possible to repeat our analysis substituting the mixed-flux R-matrix, although it will probably require a good deal of work to include the general k-dependence. This is because the functions become more complicated, and we do not have (discovered yet) all the nice properties of the (mixed-flux analog of the) Zamolodchikov dressing factor [55]. We are planning to study this problem in future work.…”

Section: Future Investigationmentioning

confidence: 99%

A study of integrable form factors in massless relativistic AdS ₃

Торриелли¹

2022

J. Phys. A: Math. Theor.

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We show that the massless integrable sector of the AdS_3 times S^3 times T^4 superstring theory, which admits a non-trivial relativistic limit, provides a setting where it is possible to determine exact minimal solutions to the form factor axioms, in integral form, based on analyticity considerations, along the same lines of ordinary relativistic integrable models. We construct in full detail the formulas for the two- and three-particle case, and show the similarities as well as the differences with respect to the off-shell Bethe ansatz procedure of Babujian et al. We show that our expressions pass a series of non-trivial consistency checks which are substantially more involved than in the traditional case. We speculate on the problems concerned in a possible generalisation to an arbitrary number of particles, and on a possible connection with the hexagon programme.

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Boost generator in AdS3 integrable superstrings for general braiding

Cited by 6 publications

References 85 publications

Yang-Baxter and the Boost: splitting the difference

Yang-Baxter and the Boost: splitting the difference

Integrable systems, separation of variables and the Yang-Baxter equation

A study of integrable form factors in massless relativistic AdS ₃

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Boost generator in AdS3 integrable superstrings for general braiding

Cited by 6 publications

References 85 publications

Yang-Baxter and the Boost: splitting the difference

Yang-Baxter and the Boost: splitting the difference

Integrable systems, separation of variables and the Yang-Baxter equation

A study of integrable form factors in massless relativistic AdS 3

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A study of integrable form factors in massless relativistic AdS ₃