DUALITY SYMMETRICAL QUANTIZATION OF SUPERSTRINGS

A general covariant quantization of a superparticle, Green-Schwarz, superstring, and a supermembrane with manifest supersymmetry and duality symmetry is proposed. This quantization provides a natural-quantum mechanical description of curved BPS-type backgrounds related to the ultrashort supersymmetry multiplets. Half-size commuting and anticommuting Killing spinors admitted by such backgrounds in quantum theory become truncated K-symmetry ghosts. The symmetry of Killing spinors under dualities transfers to the symmetry of the spectrum of states. A GS superstring in the generalized semi-light-cone gauge can be quantized consistently in the background of ten-dimensional supersymmetric gravitational waves. Upon compactification they become supersymmetric electrically charged black holes, either massive or massless. However, the generalized light-cone gauge breaks S duality. We propose a new family of gauges, which we cap black hole gauges. These gauges are suitable for quantization both in hat Minkowski space and in the black hole background, and they are duality symmetric. As an example, a manifestly S-duality symmetric black hole gauge is constructed in terms of the axion-dilaton-electric-magnetic black hole hair. We also suggest the U-duality covariant class of gauges for type II superstrings.