Two-dimensional quantum gravity and current algebra on a torus

Abstract

Two dimensional induced quantum gravity on a torus is analyzed. By introducing the non-analytic Green``S function, we evaluate the correlation functions of the metric from the Ward identity and show that the two dimensional quantum gravity on torus is still ralated to SL(2, R) cruuent algebra. We cast the supersymmetric extension to Polyakov``s work and find that the central charge of current algebra related to the (2, 0) supergravity is real for any space time dimension d. This fact is originated from the vanishing of "dimensionality" (number of boson minus number of fermion generators) of OSP(2/2) algebra.