Brst Cohomology and Physical States in 2D Supergravity Coupled to ${\hat c} \leq 1$ Matter

Abstract

We study the BRST cohomology for two-dimensional supergravity coupled to $\hat c \leq 1$ superconformal matter in the conformal gauge. The super-Liouville and superconformal matters are represented by free scalar fields $ϕ^L$ and $ϕ^M$ and fermions $ψ^L$ and $ψ^M$, 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 $N_{FP}=0,\pm 1$ for discrete momenta other than the degree of freedom corresponding to the ``center of mass&#34;, and that these are closely related to the ``null states&#34; in the minimal models with $\hat c<1$.