Related papers: Characters and relations among SW(3/2,2) algebras

Field theoretic and geometric ideas are used to construct a chiral supersymmetric field theory whose ground state is a specified irreducible representation of a centrally extended loop group. The character index of the associated…

We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic…

We consider the quantum-mechanical algebra of observables generated by canonical quantization of $SL(2,R)$ Chern-Simons theory with rational charge on a space manifold with torus topology. We produce modular representations generalizing the…

A sort of calculus is developed to find the chiral algebras of N=2 superconformal interacting bosonic models. Many examples are discussed. It is shown that the algebras share a common structure, which we call almost Landau Ginzburg. For one…

We give a construction of algebraic differential characters, receiving classes of algebraic bundles with connection, lifitng the Chern-Simons invariants defined with S. Bloch, the classes in the Chow group and the analytic secondary…

We determine the algebra of holonomy symmetries of sigma models propagating on supersymmetric heterotic backgrounds with a non-compact holonomy group. We demonstrate that these close as a W-algebra, which in turn is specified by a Lie…

We explicitly construct the extension of the N=2 super Virasoro algebra by two super primary fields of dimension two and three with vanishing u(1)-charge. Using a super covariant formalism we obtain two different solutions both consistent…

We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra)…

In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular…

We study a spectral problem related to the finite-dimensional characters of the groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$, which form the classical series $C$, $B$, and $D$, respectively. The irreducible characters of these three series are…

The realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents are reviewed. Both the N=8 and N=7 algebras admit unitary realizations in…

In this paper we continue the study of character sheaves on a reductive group G. To each subset of the set of simple reflections in the Weyl group we associate an algebra of the same kind as an Iwahori-Hecke algebra with unequal parameters…

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current $j_\mu$ associated with the global symmetry of the theory, a composite…

We use combinatorics of $qq$-characters to study extensions of deformed $W$-algebras. We describe additional currents and part of the relations in the cases of $\mathfrak{gl}(n|m)$ and $\mathfrak{osp}(2|2n)$.

We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras $W_3$ and $W_3^{(2)}$ can be embedded as subalgebras into some {\em linear} algebras with finite set of currents. Using these linear algebras we find new field…

We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight…

The characters of irreducible finite dimensional representations of compact simple Lie group G are invariant with respect to the action of the Weyl group W(G) of G. The defining property of the new character-like functions ("hybrid…

We show that the symmetry algebra of the $SL(2,R)_{k}/U(1)$ coset model is a non-linear deformation of $W_{\infty}$, characterized by $k$. This is a universal $W$-algebra which linearizes in the large $k$ limit and truncates to $W_{N}$ for…

We construct dual descriptions of (0,2) gauged linear sigma models. In some cases, the dual is a (0,2) Landau-Ginzburg theory, while in other cases, it is a non-linear sigma model. The duality map defines an analogue of mirror symmetry for…

We consider a general N=(2,2) non-linear sigma-model in (2,2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields.…