Polymer quantization of the CGHS model: I

Abstract

We present a polymer (loop) quantization of a two-dimensional theory of dilatonic gravity known as the CGHS model. We recast the theory as a parametrized free field theory on a flat two-dimensional spacetime and quantize the resulting phase space using techniques of loop quantization. The resulting (kinematical) Hilbert space admits a unitary representation of the spacetime diffeomorphism group. We obtain the complete spectrum of the theory using a technique known as group averaging and perform quantization of Dirac observables on the resulting Hilbert space. Finally, we argue that the algebra of Dirac observables gets deformed in the quantum theory.