Related papers: Conformal Current Algebra in Two Dimensions

We discuss the nonlinear extension of $N=2$ superconformal algebra by generalizing Sugawara construction and coset construction built from $N=2$ currents based on Kazama-Suzuki $N=2$ coset model $\frac{SU(3)}{SU(2) \times U(1)}$ in $N=2$…

These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the…

We construct algebraic-geometric families of genus one (i.e. elliptic) current and affine Lie algebras of Krichever-Novikov type. These families deform the classical current, respectively affine Kac-Moody Lie algebras. The construction is…

The conformal non-compact $SL(2,R)/U(1)$ coset model in two dimensions has been recently shown to embody a nonlinear $\hat{W}_\infty$ current algebra, consisting of currents of spin $\geq 2$ including the energy-momentum tensor. In this…

Superconformal ghost current generators of conformal dimension 3/2 are constructed using the conformal ghosts and anticommuting infinite dimensional gamma matrices of the Clifford algebra. The super-Virasoro algebra for the ghosts in both…

We present a systematic approach to constructing current algebras based on non-semi-simple groups. The Virasoro central charges corresponding to these current algebras are not, in general, given by integer numbers. The key point in this…

We construct the nonlinear $N=2$ super-$W_3^{(2)}$ algebra with an arbitrary central charge at the classical level in the framework of Polyakov "soldering" procedure. It contains two non-intersecting subalgebras: $N=2$ superconformal…

The sigma model describing the dynamics of the superstring in the $AdS_5 \times S^5$ background can be constructed using the coset $PSU(2,2|4)/SO(4,1)\times SO(5)$. A basic set of operators in this two dimensional conformal field theory is…

The commutator anomalies (Schwinger terms) of current algebras in $3+1$ dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra…

Previously we have established that the second Hamiltonian structure of the KP hierarchy is a nonlinear deformation, called $\hat{W}_{\infty}$, of the linear, centerless $W_{\infty}$ algebra. In this letter we present a free-field…

Motivated by recent progress on the correspondence between string theory on anti-de Sitter space and conformal field theory, we address the question of constructing space-time N extended superconformal algebras on the boundary of AdS_3.…

We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras…

We investigate the Kac-Moody algebra of noncommutative Wess-Zumino-Witten model and find its structure to be the same as the commutative case. Various kinds of gauged noncommutative WZW models are constructed. In particular, noncommutative…

We find out that some unitary minimal models of the N=1 ${\cal SW}(3/2,2)$ superconformal algebra can be realized as the level one coset models based on the Wolf spaces $SU(n)/(SU(n-2)\times SU(2))$. We obtain the expression of the…

In the present contribution, I report on certain {\it non-linear} and {\it non-local} extensions of the conformal (Virasoro) algebra. These so-called $V$-algebras are matrix generalizations of $W$-algebras. First, in the context of…

The conformal extension of the BMS$_{3}$ algebra is constructed. Apart from an infinite number of 'superdilatations,' in order to incorporate 'superspecial conformal transformations,' the commutator of the latter with supertranslations…

We investigate the quantum conformal algebras of N=2 and N=1 supersymmetric gauge theories. Phenomena occurring at strong coupling are analysed using the Nachtmann theorem and very general, model-independent, arguments. The results lead us…

We prove that the family of non-linear $W$-algebras $SW(3/2,2)$ which are extensions of the $N=1$ superconformal algebra by a primary supercurrent of conformal weight $2$ can be realized as a quantum Hamiltonian reduction of the Lie…

We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its…

We study global subalgebras of superconformal algebras in two dimensions and their unitary representations. Global superconformal multiplets are decomposed into conformal multiplets using Racah-Speiser algorithm, revealing many essential…