BRST COHOMOLOGY AND PHYSICAL STATES IN 2D SUPERGRAVITY COUPLED TO ĉ ≤ 1 MATTER

We study the BRST cohomology for two-dimensional supergravity coupled to ĉ ≤ 1 superconformal matter in the conformal gauge. The super-Liouville and superconformal matters are represented by free scalar fields φ and φ and fermions ψ and ψ , respectively, with suitable background charges, and these are coupled in such a way that the BRST charge is nilpotent. The physical states of the full theory are determined for NS and R sectors. It is shown that there are extra states with ghost number NFP = 0,±1 for discrete momenta other than the degree of freedom corresponding to the “center of mass”, and that these are closely related to the “null states” in the minimal models with ĉ < 1.