Related papers: $gl(4|4)$ current algebra: free field realization …
The $osp(2n|2n)$ current algebra for a {\it generic} positive integer $n$ at general level $k$ is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. The associated screening currents of the…
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…
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.
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…
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 non-semisimple $gl(2|2)_k$ current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible…
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…
We construct five independent screening currents associated with the $U_q(\widehat{sl(3)})$ quantum current algebra. The screening currents are expressed as exponentials of the eight basic deformed bosonic fields that are required in the…
In this letter a screening current or contour representation is given of certain quantum superalgebras. The Gomez-Sierra construction of quantum groups in conformal field theory is generalized to cover superalgebras and illustrated using…
In this thesis steps are taken in the direction of formulating non-critical strings in the framework of the $G/G$ approach. A major part of the thesis is concerned with conformal field theory based on affine $SL(2)$ current algebra, in…
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 free field representation of the gl(1|1)_k current algebra at arbitrary level k is given in terms of two scalar fields and a symplectic fermion. The primary fields for all representations are explicitly constructed using the twist and…
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…
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 screening currents of the second kind are considered. They are constructed in any affine current algebra for directions corresponding to simple roots with multiplicity one in a decomposition of the highest root on a set of…
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…
We define currents on a Grassmann algebra $Gr(N)$ with $N$ generators as distributions on its exterior algebra (using the symmetric wedge product). We interpret the currents in terms of ${\Z}_2$-graded Hochschild cohomology and closed…
The four fermionic currents of the affine superalgebra $sl(2/1)$ at fractional level $k=1/u-1$, u positive integer, are shown to be realised in terms of a free scalar field, an $sl(2)$ doublet field and a primary field of the parafermionic…
We construct level 1 basic representations of the quantized current algebras associated to higher genus algebraic curves using one free field. We also clarify the relation between the elliptic current algebras of the papers [EF] and [JKOS].
The conformal field theory for the $gl(N,N)$ affine Lie superalgebra in two space-time dimensions is studied. The energy-momentum tensor of the model, with vanishing Virasoro anomaly, is constructed. This theory has a topological symmetry…