Related papers: Kondo line defects and affine Gaudin models

The fusion products of admissible representations of the su(2) WZW model at the fractional level k=-4/3 are analysed. It is found that some fusion products define representations for which the spectrum of L_0 is not bounded from below.…

We employ the $\mathrm{SU}(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$…

We study a single channel one dimensional Kondo Model where the impurity spin is replaced by an su(n) spin. Using Abelian bosonization and canonical transformation we explicitly show that this system has an exactly solvable point. The…

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2)and SU(2)/Z_2 gauge theories, compactified on a small spatial circle R^(1,2) x S^1, and considered at…

A quantum integrable model related to $U_q(\hat{sl}(N))$ is considered. A reduced model is introduced which allows interpretation in terms of quantized affine Jacobi variety. Closed commutation relations for observables of reduced model are…

We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\Tr (\Phi_1 (z_1)\ldots \Phi_n…

Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order…

We introduce a class of quantum integrable systems generalizing the Gaudin model. The corresponding algebras of quantum Hamiltonians are obtained as quotients of the center of the enveloping algebra of an affine Kac-Moody algebra at the…

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and…

We prove the existence of a family of integrable deformations of $\mathbb{Z}_N$-coset models in two dimensions. Our approach uses and generalises the method of auxiliary fields that was recently introduced for the principal chiral model by…

We discuss the string theory on AdS_3. In the first half of this talk, we review the SL(2,R) and the SL(2,C)/SU(2) WZW models which describe the strings on the Lorentzian and Euclidean AdS_3 without RR backgrounds, respectively. An emphasis…

A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative…

We calculate the nonequilibrium conductance of a system of two capacitively coupled quantum dots, each one connected to its own pair of conducting leads. The system has been used recently to perform pseudospin spectroscopy by controlling…

In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special…

We study the "topological gauged WZW model associated with $SU(2)/U(1)$",which is defined as the twisted version of the corresponding supersymmetric gauged WZW model. It is shown that this model is equivalent to a topological conformal…

We propose an integrable system of coupled nonlinear Schrodinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short optical soliton pulse propagation in non-Kerr media. Lax pair, conserved…

The question of the integrability of real-coupling affine toda field theory on a half-line is addressed. It is found, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained.…

Twisted Hopf algebra $sl_\xi(2)$ gives rise to a deformation of the Yangian ${\cal Y}(sl(2))$. The corresponding deformations of the integrable XXX-spin chain and the Gaudin model are discussed.

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may…

We show how to resolve coherent low-energy features embedded in a broad high-energy background by use of a fully self-consistent calculation for composite particle operators. The method generalizes the formulation of Roth, which linearizes…