Related papers: $\mathcal{SW}$-algebras and strings with torsion

Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension.…

We associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of…

The most general large ${\cal N}=4$ superconformal ${\cal W}_{\infty}$ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the ${\cal W}_{\infty}$…

We obtain a bosonization prescription that allows to represent the energy-momentum tensor and supersymmetry generators of non-critical superstring theories with minimal matter as those of topological supergravity. Superstrings with $N=1$…

We perform canonical quantization of the open Neveu-Schwarz-Ramond (NSR) superstrings in the background of a D-brane with the NS B-field. If we choose the mixed boundary condition as a primary constraint, it generates a set of secondary…

The fermionic NSR string possesses a hidden N = 2 superconformal algebra on the world-sheet. In this work, we show how to use an isomorphism of this algebra, the so-called spectral flow, for construction of a subspace of physical states of…

We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally…

The SU(2) WZW model at large level N can be interpreted semiclassically as string theory on S^3 with N units of Neveu-Schwarz H-flux. While globally geometric, the model nevertheless exhibits an interesting doubled geometry possessing…

We study the classical version of supersymmetric $W$-algebras. Using the second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and $W_3$-algebras.

Certain vertex algebras and Lie algebras arising in superstring theory are investigated. We show that the Fock space of a compactified Neveu-Schwarz superstring, i.e. a Neveu-Schwarz superstring moving on a torus, carries the structure of a…

A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra…

We consider classical and quantum strings in the conformally invariant background corresponding to the SL(2,R) WZWN model. This background is locally anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as…

Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…

We quantise the classical gauge theory of $N=2\ w_\infty$-supergravity and show how the underlying $N=2$ super-$w_\infty$ algebra gets deformed into an $N=2$ super-$W_\infty$ algebra. Both algebras contain the $N=2$ super-Virasoro algebra…

The four different kinds of currents are given by the multiple $(\beta,\gamma)$ and $(b,c)$ ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation…

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic…

The main objective of this work is to construct and classify the most general classical and quantum $\mathcal{N}=1$ $\mathcal{W}_\infty$-algebras generated by the same spins as the singlet algebra of $N$ fermions and $N$ bosons in the…

We construct new heterotic string backgrounds which are analogous to superstring solutions corresponding to coset models but are not simply the `embeddings'of the latter. They are described by the (1,0) supersymmetric extension of the $G/H$…

We discuss the mathematical properties of six--dimensional non--K\"ahler manifolds which occur in the context of ${\cal N}=1$ supersymmetric heterotic and type IIA string compactifications with non--vanishing background H--field. The…

We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to the deformed Leibniz rule…