BF actions for the Husain-Kuchař model

We show that the Husain-Kuchař model can be described in the framework of $\mathrm{BF}$ theories. This is a first step towards its quantization by standard perturbative quantum field theory techniques or the spin-foam formalism introduced in the space-time description of general relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the $\mathrm{BF}$-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.