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

Abstract

We study the BRST cohomology for two-dimensional supergravity coupled to $\hat{c}\le 1$ superconformal matter in the conformal gauge. The super-Liouville and superconformal matters are represented by free scalar fields ${\varphi }^L$ and ${\varphi }^M$ and fermions ${\psi }^L$ and ${\psi }^M$, 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", and that these are closely related to the ``null states" in the minimal models with $\hat{c}<1$.

34 pages

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