Canonical approach to 2D supersymmetric WZNW model coupled to supergravity

Starting from the known representation of the Kac-Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac-Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy-momentum tensor $L_\pm$ and $G_\pm$ play the role of the diffeomorphisms and supersymmetries generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.Comment: LaTeX, 13 page

W-Strings on Curved Backgrounds

We discuss a canonical formalism method for constructing actions describing propagation of W-strings on curved backgrounds. The method is based on the construction of a representation of the W-algebra in terms of currents made from the string coordinates and the canonically conjugate momenta. We construct such a representation for a W_3-string propagating in the background metric with one flat direction by using a simple ansatz for the W-generators where each generator is a polynomial of the canonical currents and the veilbeins. In the case of a general background we show that the simple polynomial ansatz fails, and terms containing the veilbein derivatives must be added.Comment: 10 pages, Latex, no figures. Revised version (the incorrect result following from a wrong interpretation of a vielbein constraint has been corrected

Noncommutativity relations in type IIB theory and their supersymmetry

In the present paper we investigate noncommutativity of $D9$ and $D5$-brane world-volumes embedded in space-time of type IIB superstring theory. Boundary conditions, which preserve half of the initial supersymmetry, are treated as canonical constraints. Solving the constraints we obtain original coordinates in terms of the effective coordinates and momenta. Presence of momenta induces noncommutativity of string endpoints. We show that noncommutativity relations are connected by N=1 supersymmetry transformations and noncommutativity parameters are components of N=1 supermultiplet