Gravity as a constrained BF theory: Noether charges and Immirzi parameter

We derive and analyze Noether charges associated with the diffeomorphism invariance for the constrained $SO(2,3)$ BF theory. This result generalizes the Wald approach to the case of the first order gravity with a negative cosmological constant, the Holst modification, and topological terms (Nieh-Yan, Euler, and Pontryagin). We show that differentiability of the action is automatically implemented by the structure of the constrained BF model. Finally, we calculate the AdS–Schwarzschild black hole entropy from the Noether charge and we find that it does not depend on the Immirzi parameter.