Related papers: Free field realization of the $osp(2n|2n)$ current…
We construct the explicit free field representations of the current algebras $so(2n)_k$, $so(2n+1)_k$ and $sp(2n)_k$ for a generic positive integer $n$ and an arbitrary level $k$. The corresponding energy-momentum tensors and screening…
The $gl(4|4)$ current algebra at general level $k$ is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. Seven screening currents of the first kind are also presented.
The free-field representations of the $D(2,1;\a)$ current superalgebra and the corresponding energy-momentum tensor are constructed. The related screening currents of the first kind are also presented.
We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is…
Based on the particular orderings introduced for the positive roots of finite dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the $osp(2r|2n)$ and $osp(2r+1|2n)$ superalgebras and the…
The free field representation of the osp(1|2) current algebra is analyzed. The four point conformal blocks of the theory are studied. The structure constants for the product of an arbitrary primary operator and a primary field that…
The Osp(2|2) current algebra at level k=-2 is known to describe the IR fixed point of 2D Dirac fermions, subject to a random SU(2) gauge potential. We show that this theory has a simple free-field representation in terms of a compact, and a…
We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general…
We study the free field realization of the two-dimensional osp(1|2) current algebra. We consider the case in which the level of the affine osp(1|2) symmetry is a positive integer. Using the Coulomb gas technique we obtain integral…
Motivated by applications of twisted current algebras in description of the entropy of $Ads_3$ black hole, we investigate the simplest twisted current algebra $sl(3,{\bf C})^{(2)}_k$. Free field representation of the twisted algebra and the…
Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. By using these realization, the correlation functions of N=2 super-conformal model based on osp(2|2) symmetry and…
Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate $gl(2|2)$ current superalgebra at general level $k$. We construct its free field representation and…
In this paper we consider Wakimoto free field realizations of simple affine Lie algebras, a subject already much studied. We present three new sets of results. (i) Based on quantizing differential operator realizations of the corresponding…
In this paper free field realizations of affine current superalgebras are considered. Based on quantizing differential operator realizations of the corresponding basic Lie superalgebras, general and simple expressions for both the bosonic…
A graded generalization of the Z_k parafermionic current osp(1|2)/U(1) coset conformal field theory. The structure of the parafermionic highest-weight modules is analyzed and the dimensions of the fields of the theory are determined. A free…
We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson…
We construct a free field realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for arbitrary level $k \neq 0,-N$. We study Drinfeld current and the screening current associated with $U_{q,p}(\hat{sl_N})$ for arbitrary level…
Sigma models arise frequently in particle physics and condensed-matter physics as low-energy effective theories. In this paper I compute the exact free energy at any temperature in two hierarchies of integrable sigma models in two…
A representation of the quantum affine algebra $U_{q}(\hat{sl_{2}})$ of an arbitrary level $k$ is realized in terms of three boson fields, whose $q \rightarrow 1$ limit becomes the Wakimoto representation. An analogue of the screening…
Free field equations, with various spins, for space-time algebras with second-rank tensor (instead of usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. The most attention is payed to the gauge…