Introduction to Covariant Formulation of Superstring (Field) Theory

摘要

The present paper briefly discusses about covariant formulation of superstring theories based on BRS invariance. First, the Neveu-Schwarz-Ramond (NSR) model is outlined. This model describes a string on which fermions are living. Those fermions are described by two dimensional Majorana spinors, since a string spans a two dimensional surface, i.e., world sheet in the D-dimensional space-time. Discussions are then made on the relations between space-time bosons and fermions, super Virasoro algebra, no-ghost theorem, BRS charge, and supersymmetry in the NSR model Another section is devoted to describing covariant (free) field theory of superstring using the first-quantized BRS charges. Discussions are made on field theories of point particle, bosonic string and superstring, as well as space-time supersymmetry. It is concluded that field theories of closed strings including the heterotic string can be considered in similar ways. Interaction terms are constructed according to the BRS invariance of the total actions. Two kinds of them have been proposed, though the relation between them has not been clarified. Furthermore, covariant gauge fixing of interacting string field theories and/or covariant quantization have some difficulties and have not been clarified. It is also pointed out that the space-time supersymmetry would come from the 2-dimensional gauge symmetries, or could be ragarded as a part of the original string gauge symmetries. (ERA citation 13:023548)