Canonical analysis of cosmological topologically massive gravity at the chiral point

TL;DR

The paper addresses the presence of bulk degrees of freedom in cosmological topologically massive gravity at the chiral point by developing a non-perturbative canonical analysis within a novel first-order, Chern-Simons–based formulation. By selecting an efficient set of canonical variables and deriving a complete secondary constraint structure, the authors show the physical phase space per spatial point has dimension two, corresponding to one bulk degree of freedom—the topologically massive graviton. The reformulation as a difference of CS and EH terms at $$ enables a transparent constraint analysis and yields a delta-function–localized algebra, aligning with expectations from linearized studies while clarifying the full non-perturbative structure. The work highlights both the success of the Vienna School approach in simplifying gravity’s canonical treatment and the subtleties of invertibility and non-perturbative sectors in first-order CTMG.

Abstract

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, cosmological 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.