Chern–Simons-like formulation of exotic massive 3D gravity models

We investigate the Chern–Simons-like formulation of exotic general massive gravity models within the framework of third-way to three-dimensional gravity. We classify our construction into two main approaches: one using torsional cosmological Einstein and exotic massive gravity equations, and the other a torsion-free approach. The former approach, while mathematically appealing, precludes the construction of critical exotic models where the central charges vanish. In contrast, the latter approach has a wider parameter space and allows for the construction of critical models. An explicit example of an exotic general model is provided to illustrate both methods. Our methodology represents the first step towards establishing the most general Chern–Simons-like formulation of third-way to three-dimensional gravity, which would enable the study of identifying its bulk/boundary unitary sector.