相关论文: Liouville reflection operator, affine Yangian and …
This paper is devoted to study of integrable structures in superconformal field theory and more general coset CFT's related to the affine Yangian $\textrm{Y}\big(\widehat{\mathfrak{gl}}(2)\big)$. We derive the relation between the RLL and…
In these notes we study integrable structures of conformal field theory with $\textrm{BCD}$ symmetry. We realise these integrable structures as affine Yangian $\mathfrak{gl}(1)$ "spin chains" with boundaries. We provide three solutions of…
The quantum theory of the Liouville model with imaginary field is considered using the quantum inverse scattering method. An integrable structure with nontrivial spectral parameter dependence is developed for lattice Liouville theory by…
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, paperclip and KdV integrable structures, they are…
We study $\mathcal{N}=2$ superconformal field theory and define the R-matrix which acts as an intertwining operator between different realizations of $\mathcal{N}=2$ $W-$algebras of type $A$. Using this R-matrix we define $RLL$ algebra and…
We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for…
Using the example of Liouville theory, we show how the separation into left- and rightmoving degrees of freedom of a nonrational conformal field theory can be made explicit in terms of its integrable structure. The key observation is that…
In this paper we study matrix model realizations of Liouville conformal blocks with degenerate and irregular operators. The corresponding matrix model is Hermitian with a $\beta$-deformed measure and the degree of the potential corresponds…
We study the higher spin algebras of two-dimensional conformal field theory from the perspective of quantum integrability. Starting from Maulik-Okounkov instanton R-matrix and applying the procedure of algebraic Bethe ansatz, we obtain…
We introduce a class of induced representations of the degenerate double affine Hecke algebra of gl_N and analyze their structure mainly by means of intertwiners. We also construct them from modules of the affine Lie algebra using…
We consider a system of Integrals of Motion in conformal field theory related to the gl(2) Intermediate Long Wave equation. It interpolates between the system studied by Bazhanov, Lukyanov and Zamolodchikov and the one studied by the author…
We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…
We find all the diagonal $K$-matrices for the $R$-matrix associated with the minimal representation of the exceptional affine algebra $G^{(1)}_2$. The corresponding transfer matrices are diagonalized with a variation of the analytic Bethe…
In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain…
We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian $Y(X_r)$ or its quantum affine analogue $U_q(X^{(1)}_r)$ for $X_r = B_r, C_r$ and $D_r$. Eigenvalue formulas are proposed for the transfer matrices…
We present a superconformally invariant and integrable model based on the twisted affine Kac-Moody superalgebra $\hat{osp(2|2)}^{(2)}$ which is the supersymmetrization of the purely bosonic conformal affine Liouville theory recently…
We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…
We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(2|1). The…
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…