[en] The problems of finding the solutions of the super self duality equations are explained. Some prospects of an approach to self-duality in gauge theories are given

[en] I show how bosonic (free field) representations for so-called degenerate conformal theories are built by singular vectors in Verma modules. Based on this construction, general expressions of conformal blocks are proposed. This construction also yields a new kind of bosonization in 2d conformal field theories. (orig.)

[en] Short communication

[en] The choice of a coordinate chart on an analytical Rⁿ (R_aⁿ) provides a representation of the n-dimensional SUSY oscillator. The corresponding Hilbert space is Cartan's exterior algebra endowed with a suitable scalar product. The exterior derivative gives rise to the algebra of the n-dimensional SUSY oscillator. Its euclidean dynamics is an inherent consequence of the geometry imposed by the Lie derivative generating the dilations, i.e. evolution of the quantum system corresponds to parametrization of a sequence of charts by euclidean time. Coherent states emerge as a natural structure related to the Lie derivative generating the translations. (orig.)

[en] Short communication

[en] We review the conformal invariance conditions for 2D field theories both on manifolds without and with boundary. Special emphasis is given to our recent derivation of the T.T operator product expansion in the boundary case using only diffeomorphism invariance and the knowledge of the trace anomaly. (orig.)

[en] We review the construction of field operators of the N = 1 supersymmetric Liouville theory in terms of the components of a quantized free superfield. (orig.)

[en] We discuss charged string solutions of the effective equations of the D = 4 heterotic string theory with non-constant dilaton Φ and modulus φ fields. The effective action contains the generic moduli-dependent coupling function in the gauge field kinetic term and non-perturbative scalar potential. (orig.)

[en] A technique to calculate propagators in the background of a magnetic string is explained and extended to a special case of two-string background. (orig.)

[en] We present S⁷-algebras as generalized Kac-Moody algebras. A number of free-field representations is found. We construct the octonionic projective spaces OP^N. (orig.)