Review of AdS/CFT Integrability. Chapter VI.2: Yangian Algebra

Торриелли, Алессандро

doi:10.1007/s11005-011-0491-z

Cited by 24 publications

(25 citation statements)

References 79 publications

(133 reference statements)

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“…This should be very helpful in understanding and exploring further the integrability structure of our theories. Recall also that there is a Yangian algebra [37] (for reviews see [38,39]) that the classically conserved non-local charges of the PCM obey [40]. Quantum effects to their conservation properties have also been explored (for various aspects of the algebras of charges in PCM see [41,42]).…”

Section: Discussionmentioning

confidence: 99%

Integrable interpolations: From exact CFTs to non-Abelian T-duals

2014

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We derive two new classes of integrable theories interpolating between exact CFT WZW or gauged WZW models and non-Abelian T-duals of principal chiral models or geometric coset models. They are naturally constructed by gauging symmetries of integrable models. Our analysis implies that non-Abelian T-duality preserves integrability and suggests a novel way to understand the global properties of the corresponding backgrounds.Comment: 33 pages, Latex, V2: NPB version, minor changes and some references added, V3: typos below eq. (2.12) and in eq. (A.1) correcte

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Section: Discussionmentioning

confidence: 99%

Integrable interpolations: From exact CFTs to non-Abelian T-duals

2014

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“…In this paper we will further investigate the integrable structure of a two-parameter deformation of the PCM, which includes as a one-parameter subset (1.1) for the prototypical isotropic case λ ab = λδ ab . In particular, based on the underlying algebraic structure, we will show the existence of a Yangian algebra [18] (for reviews see [19][20][21]) of classically conserved non-local charges in the spirit of a similar computation for the (generalized) Gross-Neveu and the isotropic PCM in [22]. In the isotropic case, the Yangian algebra corresponds to the adjoint action on g, i.e.…”

Section: Introductionmentioning

confidence: 93%

The classical Yang–Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

et al. 2014

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We construct the Lax-pair, the classical monodromy matrix and the corresponding solution of the Yang-Baxter equation, for a two-parameter deformation of the Principal chiral model for a simple group. This deformation includes as a one-parameter subset, a class of integrable gauged WZW-type theories interpolating between the WZW model and the non-Abelian T-dual of the principal chiral model. We derive in full detail the Yangian algebra using two independent methods: by computing the algebra of the non-local charges and alternatively through an expansion of the Maillet brackets for the monodromy matrix. As a byproduct, we also provide a detailed general proof of the Serre relations for the Yangian symmetry.Dedicated to the memory of Sotirios Bonanos whose MATHEMATICA software has helped numerous researchers

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“…As noted above, the map (3.59) between generic Yangian generators and those of W ∞ is non-local. This suggests that we might be able to use (an analogue of) this relation, or rather, its inverse, to search for an alternative, local worldsheet description to the Yangians that appear in integrable spin chains [38]. It would also be particularly interesting to connect this to the work on integrability in AdS 3 /CFT 2 [39][40][41][42].…”

Section: Jhep04(2017)152mentioning

confidence: 99%

Higher spins and Yangian symmetries

Gaberdiel

Gopakumar

et al. 2017

J. High Energ. Phys.

122

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Abstract:The relation between the bosonic higher spin W ∞ [λ] algebra, the affine Yangian of gl 1 , and the SH c algebra is established in detail. For generic λ we find explicit expressions for the low-lying W ∞ [λ] modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ = 0 and λ = 1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W ∞ modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SH c generators. Given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries.

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Review of AdS/CFT Integrability. Chapter VI.2: Yangian Algebra

Abstract: We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of integrability for the N = 4 vs AdS5 X S5 correspondence

Cited by 24 publications

References 79 publications

Integrable interpolations: From exact CFTs to non-Abelian T-duals

Integrable interpolations: From exact CFTs to non-Abelian T-duals

The classical Yang–Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

Higher spins and Yangian symmetries

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