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

Abstract

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.