2+1 gravity with positive cosmological constant in LQG: a proposal for the physical state

In this paper, I investigate the possible quantization, in the context of loop quantum gravity, of three-dimensional gravity in the case of positive cosmological constant and try to make contact with alternative quantization approaches already existing in the literature. Due to the appearance of an anomaly in the constraints algebra, previously studied as a first step of the analysis, alternative techniques developed for the quantization of systems with constraints algebras not associated with a structure Lie group need to be adopted. Therefore, I introduce an ansatz for a physical state, which gives some transition amplitudes in agreement with what one would expect from the TuraevViro model. Moreover, in order to check that this state implements the right dynamics, I show that it annihilates the master constraint for the theory up to the first order in Λ. © 2011 IOP Publishing Ltd.