ONE-LOOP EFFECTIVE ACTION FOR A GENERIC 2D DILATON GRAVITY THEORY

We study the one-loop effective action for a generic two-dimensional d ilaton gravity theory conformally coupled to N matter fields. We obtai n an explicit expression for the effective action in the weak-coupling limit under a suitable restriction of the dilaton potential asymptoti cs. Our result applies to the CGHS model as well as to spherically sym metric general relativity. The effective action is obtained by using t he background-field method, and we take into account the loop contribu tions from all the fields in the classical action and from the ghosts. In the large-N limit, and after an appropriate field redefinition, th e one-loop correction takes the form of the Polyakov-Liouville action. (C) 1997 Elsevier Science B.V. PACS: 04.60.Kz; 04.70.Dy; 11.10.Kk.