Related papers: Integrals of motion from quantum toroidal algebras
We explicitly construct two classes of infinitly many commutative operators in terms of the deformed Virasoro algebra. We call one of them local integrals and the other nonlocal one, since they can be regarded as elliptic deformations of…
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 study integrals of motion for Hirota bilinear difference equation that is satisfied by the eigenvalues of the transfer-matrix. The combinations of the eigenvalues of the transfer-matrix are found, which are integrals of motion for…
We present an infinite set of non-local integrals of motion for deformed $W$-algebras of types $A_l, D_l$, and $E_{6,7,8}$. They can be regarded as a two-parameter deformation of trace of the monodromy matrix of the $g$-KdV theory.…
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of certain complexes, which are modeled on the…
We consider the problem of quantization of classical soliton integrable systems, such as the KdV hierarchy, in the framework of a general formalism of Gaudin models associated to affine Kac--Moody algebras. Our experience with the Gaudin…
We show that the Politzer theorem on the equations of motion implies approximate constraints on the quark correlator, restricting considerably, for sufficiently large Q^2, the number of independent distribution functions that characterize…
This paper is devoted to the quantum integrable structure of Wess-Zumino-Novikov-Witten models, formed by an infinite number of commuting Integrals of Motion (IMs) in their current algebra. Focusing for simplicity on the SU(2) case, we…
We extend Sklyanin's method of separation of variables to quantum integrable models associated to elliptic curves. After reviewing the differential case, the elliptic Gaudin model studied by Enriquez, Feigin and Rubtsov, we consider the…
This note provides an informal introduction, with examples, to some technical aspects of the re-normalization of measures on orbital integrals used in the work of Langlands, Frenkel-Langlands-Ng\^o, and Altug on Beyond Endoscopy. In…
We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst…
We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\hat{sl_N})$. We call one of them the integral of motion ${\cal G}_m$, $(m \in {\mathbb N})$ and the other the boundary…
We describe and compute various families of commuting elements of the matrix shuffle algebra of type $\mathfrak{gl}_{n|m}$, which is expected to be isomorphic to quantum toroidal $\mathfrak{gl}_{n|m}$. Our formulas are given in terms of…
We study the classical generalized gl(n) Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary…
We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion…
We consider the (direct sum over all $n$ of the) $K$-theory of the semi-nilpotent commuting variety of $\mathfrak{gl}_n$, and describe its convolution algebra structure in two ways: the first as an explicit shuffle algebra (i.e. a…
We describe the general strategy for lifting the Wess-Zumino-Witten model from the level of one-loop Kac-Moody $U_q(\widehat{\mathfrak{g}})_k$ to generic quantum toroidal algebras. A nearly exhaustive presentation is given for the two…
In this short note, we compute the classical limits of the quantum toroidal and the affine Yangian algebras of sl(n) by generalizing our arguments for gl(1) from arXiv:1404.5240. These results were mentioned as motivation in the recent…
The goal of this paper is to make first steps towards the quantisation of integrable non-linear sigma models using the formalism of affine Gaudin models, by approaching these theories through their conformal limits. We focus mostly on the…
We introduce a new elliptic quantum toroidal algebra $U_{q,t,p}(gl_{1,tor})$. Various representations in the quantum toroidal algebra $U_{q,t}(gl_{1,tor})$ are extended to the elliptic case including the level (0,0) representation realized…