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Integrable Coupled <math><mi>σ</mi></math> Models
https://repo.scoap3.org/record/30572
A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realizations of affine Gaudin models. In this language, one can associate integrable field theories with affine Gaudin models having arbitrarily many sites. We present the result of applying this general procedure to couple together an arbitrary number of principal chiral model fields on the same Lie group, each with a Wess-Zumino term.Delduc, F.Mon, 28 Jan 2019 17:16:08 GMThttps://repo.scoap3.org/record/30572urn:ISSN:1079-7114APS2019-01-28Three-parameter integrable deformation of ℤ 4 permutation supercosets
https://repo.scoap3.org/record/30352
A three-parameter integrable deformation of ℤ 4 permutation supercosets is constructed. These supercosets are of the form F ^ / F 0 $$ \widehat{F}/{F}_0 $$ where F 0 is the bosonic diagonal subgroup of the product supergroup F ^ = G ^ × G ^ $$ \widehat{F}=\widehat{G}\times \widehat{G} $$ . They include the AdS 3 × S 3 and AdS 3 × S 3 × S 3 supercosets. This deformation encompasses both the bi-Yang-Baxter deformation of the semi-symmetric space σ -model on ℤ 4 permutation supercosets and the mixed flux model. Truncating the action at the bosonic level, we show that one recovers the bi-Yang-Baxter deformation of the principal chiral model plus Wess-Zumino term.Delduc, F.Wed, 16 Jan 2019 16:54:10 GMThttps://repo.scoap3.org/record/30352urn:ISSN:1029-8479Springer/SISSA2019-01-14Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable σ -model
https://repo.scoap3.org/record/22579
A multi-parameter integrable deformation of the principal chiral model is presented. The Yang-Baxter and bi-Yang-Baxter σ -models, the principal chiral model plus a Wess-Zumino term and the TsT transformation of the principal chiral model are all recovered when the appropriate deformation parameters vanish. When the Lie group is SU(2), we show that this four-parameter integrable deformation of the SU(2) principal chiral model corresponds to the Lukyanov model.Delduc, F.Sat, 02 Dec 2017 01:21:22 GMThttps://repo.scoap3.org/record/22579urn:ISSN:1029-8479Springer/SISSA2017-10-31Affine q -deformed symmetry and the classical Yang-Baxter σ -model
https://repo.scoap3.org/record/19488
The Yang-Baxter σ -model is an integrable deformation of the principal chiral model on a Lie group G . The deformation breaks the G × G symmetry to U(1) rank( G ) × G . It is known that there exist non-local conserved charges which, together with the unbroken U(1) rank( G ) local charges, form a Poisson algebra , which is the semiclassical limit of the quantum group U q g $$ {U}_q\left(\mathfrak{g}\right) $$ , with g $$ \mathfrak{g} $$ the Lie algebra of G . For a general Lie group G with rank( G ) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra , the classical analogue of the quantum loop algebra U q L g $$ {U}_q\left(L\mathfrak{g}\right) $$ , where L g $$ L\mathfrak{g} $$ is the loop algebra of g $$ \mathfrak{g} $$ . Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ -model.Delduc, F.Mon, 27 Mar 2017 16:50:27 GMThttps://repo.scoap3.org/record/19488urn:ISSN:1029-8479Springer/SISSA2017-03-23On the Hamiltonian integrability of the bi-Yang-Baxter σ -model
https://repo.scoap3.org/record/14780
The bi-Yang-Baxter σ -model is a certain two-parameter deformation of the principal chiral model on a real Lie group G for which the left and right G -symmetries of the latter are both replaced by Poisson-Lie symmetries. It was introduced by C. Klimčík who also recently showed it admits a Lax pair, thereby proving it is integrable at the Lagrangian level. By working in the Hamiltonian formalism and starting from an equivalent description of the model as a two-parameter deformation of the coset σ-model on G × G/G diag , we show that it also admits a Lax matrix whose Poisson bracket is of the standard r/s -form characterised by a twist function which we determine. A number of results immediately follow from this, including the identification of certain complex Poisson commuting Kac-Moody currents as well as an explicit description of the q -deformed symmetries of the model. Moreover, the model is also shown to fit naturally in the general scheme recently developed for constructing integrable deformations of σ-models. Finally, we show that although the Poisson bracket of the Lax matrix still takes the r/s -form after fixing the G diag gauge symmetry, it is no longer characterised by a twist function.Delduc, F.Wed, 16 Mar 2016 14:48:38 GMThttps://repo.scoap3.org/record/14780urn:ISSN:1029-8479Springer/SISSA2016-03-15Integrable double deformation of the principal chiral model
https://repo.scoap3.org/record/5236
We define a two-parameter family of integrable deformations of the principal chiral model on an arbitrary compact group. The Yang–Baxter σ -model and the principal chiral model with a Wess–Zumino term both correspond to limits in which one of the two parameters vanishes.Delduc, F.Thu, 18 Dec 2014 14:27:29 GMThttps://repo.scoap3.org/record/5236urn:ISSN:0550-3213Elsevier2015-02Derivation of the action and symmetries of the q -deformed AdS 5 × S 5 superstring
https://repo.scoap3.org/record/4501
We recently proposed an integrable q -deformation of the AdS 5 × S 5 superstring action. Here we give details on the hamiltonian origin and construction of this deformation. The procedure is a generalization of the one previously developed for deforming principal chiral and symmetric space σ -models. We also show that the original p s u 2 , 2 | 4 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right) $$ symmetry is replaced in the deformed theory by a classical analog of the quantum group U q p s u 2 , 2 | 4 $$ {U}_q\left(\mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right)\right) $$ with q real. The relation between q and the deformation parameter η entering the action is given. The framework used to derive the deformation also enables to prove that at the hamiltonian level, the “maximal deformation” limit corresponds to an undeformed semi-symmetric space σ -model with bosonic part dS 5 × H 5 . Finally, we discuss the various freedoms in the construction.Delduc, F.Thu, 23 Oct 2014 19:15:56 GMThttps://repo.scoap3.org/record/4501urn:ISSN:1029-8479Springer/SISSA2014-10-23