Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian

@inproceedings{Litvinov2021IntegrableSO,
  title={Integrable structure of BCD conformal field theory and boundary Bethe ansatz for affine Yangian},
  author={Alexey Vad. Litvinov and Ilya Vilkoviskiy},
  year={2021}
}
In these notes we study integrable structures of conformal field theory with BCD symmetry. We realise these integrable structures as affine Yangian gl(1) ”spin chains” with boundaries. We provide three solutions of Sklyanin KRKR equation compatible with affine Yangian R-matrix and derive Bethe ansatz equations for the spectrum. 

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References

SHOWING 1-10 OF 27 REFERENCES
Integrable Structure of Conformal Field Theory III. The Yang–Baxter Relation
Abstract:In this paper we fill some gaps in the arguments of our previous papers [1,2]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining
On dual description of the deformed O(N) sigma model
A bstractWe study dual strong coupling description of integrability-preserving deformation of the O(N) sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion
Spectral Determinants for Schrödinger Equation and Q-Operators of Conformal Field Theory
Relation between the vacuum eigenvalues of CFT Q-operators and spectral determinants of one-dimensional Schrödinger operator with homogeneous potential, recently conjectured by Dorey and Tateo for
Boundary conditions for integrable quantum systems
A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open
Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz
AbstractWe construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight
Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
Abstract:This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf
Spectrum of the reflection operators in different integrable structures
The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so- called Fateev, quantum AKNS,
Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations
The spectral determinant D(E) of the quartic oscillator is known to satisfy a functional equation. This is mapped onto the A3-related Y-system emerging in the treatment of a certain perturbed
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