Abstract
The BRST cohomology of two-dimensional gravity coupled to 0≤c<1 minimal conformal matter is investigated in the conformal gauge. We formulate a general procedure to write down the physical states via the technique of spectral sequences. Paying attention to the ghost sectors, we show that the physical states correspond to the microscopic loops, and the macroscopic loops are described by b-ghosts and c-ghosts respectively. For pure gravity, several physical states are first calculated explicitly and, in addition, the general formula for macroscopic loops is obtained by relating it to a simpler Lie algebra cohomology. We also discuss the local operator algebras of microscopic loops in Liouville theory, the so-called ground ring, in the relation to those from the Schwinger-Dyson equation in the matrix model.
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