QUANTIZATION OF THE 2d EFFECTIVE GRAVITY IN THE GEOMETRICAL FORMULATION

Abstract

There exist various formulations to discuss the 2d effective gravity: (i) light-cone gauge formulation; (ii) geometrical formulation; (iii) formulation by the constrained WZWN model; and (iv) conformal gauge formulation. In the formulations other than the last one, quantization of the 2d effective gravity is not complete in the sense that either the central charges of both sectors are not known, or one of them is known but not the other. We will provide a thorough argument on quantization of the 2d effective gravity in the formulation (ii). The argument will allow us to complete the quantization in the formulation (iii), and establish the relations among the formulations (ii)-(iv) at the quantum level.