On a Canonical Quantization of Pure AdS3 Gravity

Massimo Porrati (New York)

I review results and open issues of the canonical "constrain-first" approach to pure gravity in AdS3. In particular, I examine the connection with quantization of Teichmuller space, Liouville CFT, and the role of large diffeomorphisms. The main result is a well defined proposal for the scalar product of the Hilbert space of pure gravity. By requiring normalizability of the wave function we find novel constraints on the would-be holographic dual of pure gravity. I will discuss features, consequences and problems of the approach and show how the case of highly curved AdS3 may solve some of its problems.