Related papers: Quantum line operators from Lax pairs
In a $\mathcal{N}=2$ superconformal gauge theory with matter hypermultiplets transforming in the symmetric and anti-symmetric representations of SU($N$), we study the integrated correlators of two Coulomb-branch operators and two moment-map…
We propose the full system of Baxter Q-functions (QQ-system) for the integrable spin chains with the symmetry of the $D_r$ Lie algebra. We use this QQ-system to derive new Weyl-type formulas expressing transfer matrices in all symmetric and…
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
Intertwiners between representations of Lie groups can be used to obtain relations for matrix elements. We apply this technique to obtain different identities for the wave functions of the open Toda chain, in particular raising operators…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian…
Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer…
Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if…
Quantum $A_2$-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the…
High rank solutions to the 2D Toda Lattice System are constructed simultaneously with the effective calculation of coefficients of the high rank commuting ordinary difference operators. Our technic is based on the study of discrete dynamics…
We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of…
We continue to investigate the relationship between the infrared physics of N=2 supersymmetric gauge theories in four dimensions and various integrable models such as Gaudin, Calogero-Moser and quantum spin chains. We prove interesting…
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators is…
Quantum corrections to three-point functions of scalar single trace operators in planar N=4 Super-Yang-Mills theory are studied using integrability. At one loop, we find new algebraic structures that not only govern all two loop corrections…
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined…
The modern study of singular integral operators on curves in the plane began in the 1970's. Since then, there has been a vast array of work done on the boundedness of singular integral operators defined on lower dimensional sets in…
We study two-dimensional integrable field theories from the viewpoint of the four-dimensional Chern-Simons-type gauge theory introduced recently. The integrable field theories are realized as effective theories for the four-dimensional…
In this paper the relation between 2d topological gauge theories and Bethe Ansatz equations is reviewed. In addition we present some new results and clarifications. We hope the relations discussed here are particular examples of more…
The course of 5 lectures given at the seminar "Integrable Systems: from Classical to Quantum" (Universite de Montreal, Jul 26 -- Aug 6, 1999) contains a detailed comment on the recently discovered (Gaudin-Pasquier, 1992) connection between…
This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in the discussion is the construction of quantum fields using…