Related papers: A Finite Dimensional Gauge Problem in the WZNW Mod…
We discuss D-branes on a line of conformal field theories connected by an exact marginal deformation. The line contains an SU(2) WZW model and two mutually T-dual SU(2)/U(1) cosets times a free boson. We find the D-branes preserving a U(1)…
It is shown that in the presence of a nonvanishing cosmological constant, Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ algebra of soft graviton symmetries is modified in a simple way. The deformed algebra contains a subalgebra…
It is shown, at the level of the classical action, that the Wess-Zumino-Witten-Novikov model is equivalent to a combined BF theory and a Chern-Simons action in the presence of a unique boundary term. This connection relies on the techniques…
An electroweak model in which the masses of the W and Z bosons and the fermions are generated by quantum loop graphs through a symmetry breaking is investigated. The model is based on a regularized quantum field theory in which the quantum…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
We review the construction of extended ( N=2 and N=4 ) superconformal algebras over triple systems and the gauged WZW models invariant under them. The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems (FTS) admit…
For the vanishing deformation parameter $\lambda$, the full structure of the (anti)commutator relations in the ${\cal N}=4$ supersymmetric linear $W_{\infty}[\lambda=0]$ algebra is obtained for arbitrary weights $h_1$ and $h_2$ of the…
Let $\mathbb{k}$ be a field, and let $\Lambda$ be a (not necessarily finite dimensional) $\mathbb{k}$-algebra. Let $V$ be a left $\Lambda$-module such that is finite dimensional over $\mathbb{k}$. Assume further that $V$ has a weak…
Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…
This paper establishes several fundamental structural properties of the $q$-Heisenberg algebra $\mathfrak{h}_n(q)$, a quantum deformation of the classical Heisenberg algebra. We first prove that when $q$ is not a root of unity, the global…
The technique of $Q$-polinomials are used to derive the $w$- constraints in the two-matrix and Kontsevich-like model at finite $N$. These constraints are closed and form Lie algebra. They are associated with the matrices, $\lambda…
We analyse the Witten-Woronowicz's type deformations of the Lie superalgebra osp(2,2) and obtain a deformation parametrized by three independent parameters. For some of these algebras, finite dimensional representations are formulated in…
We study quantum aspects of the recently constructed doubly lambda-deformed sigma-models representing the effective action of two WZW models interacting via current bilinears. We show that although the exact beta-functions and current…
In Physics and in Mathematics $\mathbb{Z}_2^n$-gradings, $n \geq 2$, do appear quite frequently. The corresponding sign rules are determined by the `scalar product' of the involved $\mathbb{Z}_2^n$-degrees. The present paper is the first of…
Duality groups as (spontaneously broken) gauge symmetries for toroidal backgrounds, and their role in ($\infty$-dimensional) underlying string gauge algebras are reviewed. For curved backgrounds, it is shown that there is a duality in the…
We describe solutions of 10-dimensional supergravity comprising null deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$ Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by dimensional reduction…
By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a…
Starting from flat two-dimensional gauge potentials we propose the notion of ${\cal W}$-gauge structure in terms of a nilpotent BRS differential algebra. The decomposition of the underlying Lie algebra with respect to an $SL(2)$ subalgebra…
We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…