Lorentz symetry breaking in gravity and dimensional reduction

Abstract

We propose a modification of the standard Einstein theory in four dimensions, alternative to Ref. [2], since it is based on the first order (Einstein-Cartan) approach to General Relativity, whose gauge structure is explicit. A new topological term is introduced in the sector of coupling with matter and a Lorentz symmetry breaking is induced through a mechanism proposed in a recent paper [1]. An effective planarity may be observed in the resulting theory which resembles some aspects of holography. We finally remark some related proposals and open questions which are being developed and shall be discussed in forthcoming works.