In this paper, we study the three-dimensional minimal massive gravity (MMG) in the Hamiltonian formalism. At first, we define the canonical gauge generators as building blocks in this formalism and then derive the canonical expressions for the asymptotic conserved charges. The construction of a consistent asymptotic structure of MMG requires introducing suitable boundary conditions. In the second step, we show that the Poisson bracket algebra of the improved canonical gauge generators produces an asymptotic gauge group, which includes two separable versions of the Virasoro algebras. For instance, we study the Banados-Teitelboim-Zanelli (BTZ) black hole as a solution of the MMG field equations, and the conserved charges give the energy and angular momentum of the BTZ black hole. Finally, we compute the black hole entropy from the Cardy formula in the dual conformal field theory and show our result is consistent with the value obtained by using the Smarr formula from the holographic principle.

• Received 17 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.064044