Lorentz symmetry violation in 2+1 dimensional Chern-Simons gravity

Full text: In this work, it is proposed the influence of the Lorentz symmetry violation in the (2+1) dimensional Chern-Simons gravity. It is used the correspondence between the gravity in (2+1) dimensions and the Chern-Simons action, in the way that the gauge field is described in terms of dreibein and spin connection regarded as dynamical variables of gravity and written in the adjoint representation of ISO(2,1), the Poincare group in (2+1) dimensions. It is used the Lorentz violation term proposed by Jackiw, which corresponds a Chern-Simons term including a constant vector field, invariant under active transformation, which keeps a preferential direction on the space-time and leads to a violation of the Lorentz symmetry. For this work it is taken the non-Abelian version of the Chern-Simons model. The procedure uses the Poincare group in (3+1) dimension and truncated the algebra to (2+1) dimensions through the Lorentz violation process. One space-like dimension is taken to be reduced using the method by Scherk. It is investigated the influence on the (2+1) model of a Poincare algebra in (3+1) space-time with one violated space-like dimension. To the building of the action the Casimir matrix is identified through the algebra and then it is found out the quadratic invariant term. It is noted the presence of new fields provided by the fourth dimension and the influence of the space-like extra dimension in the model. (author)