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

TL;DR

This paper analyzes the BRST cohomology in 2D supergravity coupled to matter with central charge less than or equal to one, identifying physical states and their relation to null states in minimal models.

Contribution

It provides a detailed computation of the BRST cohomology and physical states in 2D supergravity with $\uhat c \, extless\= 1$, revealing additional states linked to null states.

Findings

Extra states with ghost number 0, ±1 for discrete momenta identified.

Physical states correspond to null states in minimal models.

BRST cohomology structure clarified for supergravity with $\uhat c \, extless\= 1$.

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 $\phi^L$ and $\phi^M$ 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 $\hat c<1$.