Rodrigo F. Sobreiro

In this work, we propose a topological quantum field theory phase for four-dimensional gravity. We show it is able to generate, not only General Relativity, but the whole family of Lovelock–Cartan theories of gravity. This is accomplished due to the existence of a topological symmetry which, when explicitly broken via the introduction of a mass scale, releases the local degrees of freedom of gravity. Additionally, we introduce an extended notion of the (anti-)self-dual Landau gauge conditions to evaluate the Ward identities, counterterms, and prove the quantum stability of the model, to all orders in perturbation theory, using the algebraic renormalization technique.

In the works of Achúcarro and Townsend and also by Witten, a duality between three-dimensional Chern–Simons gauge theories and gravity was established. In all cases, the results made use of the field equations. In a previous work, we were capable of generalizing Witten’s work to the off-shell cases, as well as to the four-dimensional Yang–Mills theory with de Sitter gauge symmetry. The price we paid is that curvature and torsion must obey some constraints under the action of the interior derivative. These constraints implied on the partial breaking of diffeomorphism invariance. In this work, we first formalize our early results in terms of fiber bundle theory by establishing the formal aspects of the map between a principal bundle (gauge theory) and a coframe bundle (gravity) with partial breaking of diffeomorphism invariance. Then, we study the effect of the constraints on the homology defined by the interior derivative. The main result is the emergence of a non-trivial homology in Riemann–Cartan manifolds.

In this work we consider a fermionic quantum gas within a Lorentz-violating background at finite temperature. We derive the effective action within path integral formalism considering the interaction of external electromagnetic field and Lorentz-violating background fields with quantum fermions. To introduce the temperature effects, we employ the Matsubara formalism. Comments about the corresponding phenomenology are also made.

In the works of A. Ach\'ucarro and P. K. Townsend and also by E. Witten, a duality between three-dimensional Chern-Simons gauge theories and gravity was established. In all cases, the results made use of the field equations. In a previous work, we were capable to generalize Witten's work to the off-shell cases, as well as to four dimensional Yang-Mills theory with de Sitter gauge symmetry. The price we paid is that curvature and torsion must obey some constraints under the action of the interior derivative. These constraints implied on the partial breaking of diffeomorphism invariance. In the present work, we, first, formalize our early results in terms of fiber bundle theory by establishing the formal aspects of the map between a principal bundle (gauge theory) and a coframe bundle (gravity) with partial breaking of diffeomorphism invariance. Then, we study the effect of the constraints on the homology defined by the interior derivative. The main result is the emergence of a nontrivial homology in Riemann-Cartan manifolds.

In this work we consider the Einstein–Hilbert action in the first order order formalism coupled to Dirac spinors. From the little group symmetry, we derive the corresponding Bargmann–Wigner current which is conserved but not gauge invariant. Therefore, we construct a gauge invariant version of the Bargmann–Wigner current which is not conserved but potentially observable. Because it is not conserved we split this current into fermionic and gravitational sectors and derive their broken continuity equations for each sector. These equations compose the master equations governing the interaction of spin-currents with gravity. Furthermore, we derive the corresponding master equations in the weak field approximation.

Two-dimensional pure electrodynamics is mapped into two-dimensional gravity in the first-order formalism at classical and quantum levels. Due to the fact that the degrees of freedom of these two theories do not match, we are enforced to introduce extra fields from the beginning. These fields are introduced through a BRST exact boundary term, so they are harmless to the physical content of the theory. The map between electromagnetism and gravity fields generate a non-trivial Jacobian, which brings extra features (but also harmless to the physical content of the gravity theory) at quantum level.