THE BRST-ANTIBRACKET COHOMOLOGY OF 2D GRAVITY CONFORMALLY COUPLED TO SCALAR MATTER

We compute completely the BRST-antibracket cohomology on local functio nals in two-dimensional Weyl-invariant gravity for given classical fie ld content (two-dimensional metric and scalar matter fields) and gauge symmetries (two-dimensional diffeomorphisms and local Weyl transforma tions). This covers the determination of all classical actions, of all their rigid symmetries, of all background charges and of all candidat e gauge anomalies. In particular we show that the antifield dependence can be entirely removed from the anomalies and that, if the target sp ace has isometries, the condition for the absence of matter-field-depe ndent Weyl anomalies is more general than the familiar 'dilaton equati ons'.