Canonical analysis of cosmological topologically massive gravity at the chiral point

Wolfgang Kummer was a pioneer of two-dimensional gravity and a strong advocate of the first order formulation in terms of Cartan variables. In the present work we apply Wolfgang Kummer's philosophy, the 'Vienna School approach', to a specific three-dimensional model of gravity, cos-mological topologically massive gravity at the chiral point. Exploiting a new Chern–Simons representation we perform a canonical analysis. The dimension of the physical phase space is two per point, and thus the theory exhibits a local physical degree of freedom, the topologically massive graviton. Gravity in lower dimensions provides an excellent expedient for testing ideas about classical and quantum gravity in higher dimensions. The lowest spacetime dimension where gravity can be described is two, and Wolfgang Kummer contributed significantly to research on two-dimensional gravity, see Ref. 1 for a review. Those who knew Wolfgang will recall that one of his main points was to advocate a gauge theoretic approach towards gravity, see Ref. 2 for his last proceedings contributions. Instead of using the metric, g µν , as fundamental field he insisted on employing the Cartan variables, Vielbein e a µ and connection ω a b µ. His approach greatly facilitated the canonical analysis and the quantization of the theory. In the present work we shall study gravity in three dimensions along *