Duality Symmetric Quantization of Superstring

TL;DR

The paper introduces a covariant quantization method for superstrings and supermembranes that preserves supersymmetry and duality symmetries, enabling consistent quantum descriptions of complex backgrounds like black holes.

Contribution

It develops a duality symmetric quantization framework for superstrings and superparticles, including new gauges compatible with dualities and curved backgrounds.

Findings

Quantization in duality-symmetric gauges is consistent in curved backgrounds.

Black hole gauges preserve duality symmetries during quantization.

Superstring backgrounds can be described with manifest supersymmetry and duality invariance.

Abstract

A general covariant quantization of 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 ultra-short supersymmetry multiplets. Half-size commuting and anticommuting Killing spinors admitted by such backgrounds in quantum theory become truncated $\kappa$-symmetry ghosts. The symmetry of Killing spinors under dualities transfers to the symmetry of the spectrum of states. 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 call black hole gauges. These gauges are suitable for quantization both in flat 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.