COUPLING OF TACHYONS AND DISCRETE STATES IN C = 1 2-DIMENSIONAL GRAVITY

All the three-point couplings involving tachyons and/or discrete state s are obtained in c = 1 two-dimensional (2D) quantum gravity by means of the operator product expansion (OPE). Cocycle factors are found to be necessary in order to maintain the analytic structure of the OPE, a nd are constructed explicitly both for discrete states and for tachyon s. The effective action involving tachyons and discrete states is work ed out to summarize all of these three-point couplings.