ON THE BRST APPROACH TO 2-DIMENSIONAL GRAVITY IN THE LIGHT-CONE GAUGE

The BRST approach to two-dimensional gravity coupled to conformal field theories is discussed. The ordinary BRST symmetry acts only on the left-moving sector of the theory. It is found that there exists a BRST-like symmetry also in the right-moving sector. The conserved charge of this new symmetry is found to be nilpotent. This symmetry is a result of a redundancy of the parametrization of the gravitational field in terms of a scalar field. We propose that the physical states of the theory should belong to the cohomology of this BRST-like charge to eliminate the redundancy. It is also discussed how to derive the BRST charge from the action and the transformation laws of fields.