EFFECTIVE ACTION FOR INDUCED GRAVITY ON A 2-DIMENSIONAL MANIFOLD

Abstract

The generating functional of the correlation functions of the stress energy-tensor in conformal field theory is explicitly constructed first on the Euclidean plane and then on an arbitrary Riemann surface. For the first case, one finds “anti-holomorphic” SL(2C) symmetry as the counterpart of the SL(2C) current algebra of Polyakov’s quantized gravity in 2 dimensions. For a general real 2-dimensional manifold, one expects a fundamental change due to the breaking of SL(2C) symmetry and to loss of locality.