Generalized Husain-Kuchar models in manifolds with boundaries

In this talk, I will present a family of generalization of some well-known theories such as the Pontryagin model, the Husain-Kuchar model, or different formulations of 3-dimensional GR with cosmological constant. When boundaries are included, this family presents an interesting holographic principle: we could obtain relevant theories in both the bulk and the boundary [1]. I will address the interplay between them within the Hamiltonian framework. I will also explain the appearance of some sectors of the phase space in which the dynamics are different. Generalizations of the Pontryagin and Husain-Kuchar actions to manifolds with boundary J. Fernando Barbero G., Bogar Díaz, Juan Margalef-Bentabol, Eduardo J.S. Villaseñor Journal of High Energy Physics 10 (2019) 121 [arXiv:1906.09820]