Related papers: Free Field Construction for the ABF Models in Regi…
We give a realization of the quantum affine Lie algebras $\uqa$ and $\uqc$ in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter $q$ being related to the statistical parameter…
In this work we introduce a novel q-deformation of the Virasoro algebra expressed in terms of free fermions, we then realize that this algebra, when the deformation parameter is a root of unity can be realized exactly on the lattice. We…
We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…
From one point of view in the quantum theory of fields, free quantum fields are uniquely determined, not by field equations, but by the transformations of the field and the annihilation and creation operators from which the field is…
Free field representations of vertex algebra in SL(2,R)/U(1) x U(1) WZNW model are constructed by considering a twisted version of the Bershadsky-Kutasov free field description of discrete states in the two-dimensional black hole CFT. These…
Following recent advances in large N matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results…
In these lectures, we study and compare two different formulations of $SU(2)$, level $k=1$, Wess-Zumino-Witten conformal field theory. The first, conventional, formulation employs the affine symmetry of the model; in this approach…
Heavy-light mesons, heavy quarkonium and doubly heavy baryons are briefly discussed. Effective field theories (EFTs) of QCD based on the heavy quark mass expansion 1/m_Q provide a unified framework to describe all three systems. They…
We discuss the relations between (topological) quantum field theories in 4 dimensions and the theory of 2-knots (embedded 2-spheres in a 4-manifold). The so-called BF theories allow the construction of quantum operators whose trace can be…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
Pseudoaffine theories are characterized by formal replacement of the level to the fractional number: $k\to\frac{k}{q}$, where $q$ is integer strange to $k(g+k)$ ($g$ - dual Coxeter number). An example of "forbidden" $q$ is considered…
In this paper we will prove a series of $q$-identities suggested by the realisation of certain conformal field theories by so-called `coupled free fermions'. We will consider $q$-series arising from coupled free fermions constructed by the…
We give a simple and direct construction of a massless quantum field with arbitrary discrete helicity that satisfies Wightman axioms and the corresponding relativistic wave equation in the distributional sense. We underline the mathematical…
The Wess-Zumino-Witten model defined on the group SU(2) has a unique (non-trivial) simple current of conformal dimension k/4 for each level k. The extended algebra defined by this simple current is carefully constructed in terms of…
We show how to deal with screening charges involving fractional powers of free fields. This enables us to use the free field Wakimoto construction to obtain complete expressions for integral representations of conformal blocks for N-point…
We further define two-parameter quantum affine algebra $U_{r,s}(\widehat{\frak {sl}_n})$ $(n>2)$ after the work on the finite cases (see [BW1], [BGH1], [HS] & [BH]), which turns out to be a Drinfel'd double. Of importance for the quantum…
The spin-1/2 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We…
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the…
Our goal is to develop a more general scheme for constructing integrable lattice regularisations of integrable quantum field theories. Considering the affine Toda theories as examples, we show how to construct such lattice regularisations…
At the beginning of the 70's, Baxter introduced a multiparametric generalization of the six-vertex model. This integrable system has been found to exhibit a remarkable variety of critical behaviors. The work is part of a series of papers…