The role of quantized 2-dim. Gravity in string theory

Abstract

We present a formulation of string theory in which the 2-dim. metric is exactly quantized in the framework of SL(2, R) current algebra. In this way we replace the conformal invariance prescription by the principle of reparametrization invariance. The theory is formulated in arbitrary number of dimensions since the usual restriction of fixed matter central charge is not present. As a concrete illustration of our approach, we show that in 25 Euclidean dimensions the usual amplitudes of the 26-dimensional bosonic string theory arise. The extra time-like dimension emerges as a mode of the 2-dim. metric and the gravitational dressing of vertex operators gives rise to their time dependence.