Lorentz-violating Yang-Mills theory: discussing the Chern-Simons-like term generation

We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable.Comment: 16 pages. No figures. Final version to appear in the Eur.Phys.J.

Constrained gauge-gravity duality in three and four dimensions

The equivalence between Chern-Simons and Einstein-Hilbert actions in three dimensions established by A.~Ach\'ucarro and P.~K.~Townsend (1986) and E.~Witten (1988) is generalized to the off-shell case. The technique is also generalized to the Yang-Mills action in four dimensions displaying de Sitter gauge symmetry. It is shown that, in both cases, we can directly identify a gravity action while the gauge symmetry can generate spacetime local isometries as well as diffeomorphisms. The price we pay for working in an off-shell scenario is that specific geometric constraints are needed. These constraints can be identified with foliations of spacetime. The special case of spacelike leafs evolving in time is studied. Finally, the whole set up is analyzed under fiber bundle theory. In this analysis we show that a traditional gauge theory, where the gauge field does not influence in spacetime dynamics, can be (for specific cases) consistently mapped into a gravity theory in the first order formalism.Comment: 25 pages. No figures. Final version accepted for publication at the European Physical Journal

Topological gauge-gravity equivalence: fiber bundle and homology aspects

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. First (Ach\'ucarro and Townsend), by considering an In\"on\"u-Wigner contraction from a superconformal gauge theory to an Anti-de Sitter supergravity. Then, Witten was able to obtain, from Chern-Simons theory (in two cases: Poincar\'e and de Sitter gauge theories), an Einstein-Hilbert gravity by mapping the gauge symmetry in local isometries and diffeomorphisms. In all cases, the results made use of the field equations. Latter, we were capable to generalize Witten's work (in Euclidean spacetime) 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 result being the emergence of a nontrivial homology in Riemann-Cartan manifolds.Comment: 14 pages; 5 figure

Fermionic quantum gas at finite temperature within a Lorentz violating background

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.Comment: 10 pages, no figure