Local symmetries and physical degrees of freedom in f(T) gravity: A Dirac-Hamiltonian constraint analysis

In the literature on f(T) gravity, the status of local Lorentz invariance and the number of physical degrees of freedom have been controversial issues. Relying on a detailed Hamiltonian analysis, we show that local Lorentz invariance is completely broken, whereas, generically, the number of physical degrees of freedom is N* = 5; in D dimensions, this number is N* = D(D - 3)/2 + (D - 1). As expected, the theory is vulnerable to having problematical propagating modes. We compare our results with those existing in the literature. As a by-product of our analysis, the diffeomorphism invariance is explicitly confirmed.