On integrable deformations of the Cherednik model

Ctirad Klimcik

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On integrable deformations of the Cherednik model

Ctirad Klimcik

High Energy Physics - Theory · Submitted 1 Sep 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.

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We provide the E-model formulation of the non-deformed Cherednik model as well as of its Poisson-Lie and Poisson-Lie-WZ deformed version. In all three cases we solve the sufficient condition of integrability by using the E-model formalism. We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We provide the E-model formulation of the non-deformed Cherednik model as well as of its Poisson-Lie and Poisson-Lie-WZ deformed version.	contribution 0.96	0.93	0.12	asserted 1.00
s1	In all three cases we solve the sufficient condition of integrability by using the E-model formalism.	method 0.69	0.94	0.33	asserted 1.00
s2	We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.	interpretation 0.38	0.88	0.60	asserted 1.00

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Original abstract

We provide the E-model formulation of the non-deformed Cherednik model as well as of its Poisson-Lie and Poisson-Lie-WZ deformed version. In all three cases we solve the sufficient condition of integrability by using the E-model formalism. We thus recover in an alternative way the known results for the non-deformed and the Poisson-Lie deformed models, while for the Poisson-Lie-WZ deformed one our results are new.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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This means that we formulate each of the three models as the $$-models on appropriate Drinfeld doubles and then we try to find out whether a sufficient condition of $$-model integrability [ref] can be applied.

On integrability of 2-dimensional $\sigma$-models of Poisson-Lie type · Introduction · 0.97

Compares with 3 papers

In the case of the first two families [ref] and [ref], a suitable ansatz for the $$-model Lax matrix completely reproduces the results of [ref] which were obtained by non-$$-models methods.

An elliptic integrable deformation of the Principal Chiral Model · Introduction · 0.97
In the case of the first two families [ref] and [ref], a suitable ansatz for the $$-model Lax matrix completely reproduces the results of [ref] which were obtained by non-$$-models methods.

Integrability and renormalizability for the fully anisotropic ${\rm SU}(2)$ principal chiral field and its deformations · Introduction · 0.97
We choose the basis of $$ as $T_A$, $A=1,…, 6$ [equation] Using the notation of Section 2.3, we then find [equation] [equation] [equation] Inserting all this in [ref], we obtain precisely the RG flows of the couplings $D_1,D_2,D_3$ which were obtained in [ref] without using the $$-models formalism: dD_1/dμ=-4K^2K^3/D_2D_3, dD_2/dμ=-4K^3K^1/D_3D_1, dD_3/dμ=-4K^1K^2/D_1D_2.

Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model · RG flow of the non-deformed model · 0.98

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