de Sitter group and Einstein-Hilbert Lagrangian

Abstract

Axial vector torsion in the Einstein-Cartan space U 4 is considered here. By picking a particular term from the SO(4, 1) Pontryagin density and then modifying it in a SO(3, 1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsion-less connection as independent fields, it has been found that κ and λ of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that κ has been found to be linked with the topological Nieh-Yan density of U 4 space.

Induced gravity from gauge theories

“…In any of these cases, the Yang-Mills action [25] is not considered. When the Yang-Mills action is taken into account, the starting theory is already metric dependent, see for instance [26,27]. Only in [28], the Yang-Mills was considered independently of the metric.…”

Gauge theories and gravity

“…To circumvent these problems, by generalizing the gauge groups and their respective actions, many other theories have been proposed. For instance, as discussed in [5,6,7,8,9], spontaneous symmetry breaking based on a Higgs-like mechanism was used to make the vierbein emerge. In these works, besides de Sitter groups, several groups were considered, as well as different starting actions that encode gravity as a limit.…”

de Sitter gauge theories and induced gravities

“…In particular, it is worth mentioning the de Sitter groups SO(m, n), with (m + n) = 5, in fourdimensional spacetime [9,10,11], need a gauge symmetry breaking; in this way the vierbein can emerge. The most used method for the breaking is the Higgs mechanism, which needs an extra set of scalar fields, see for instance [9,10,11,12,13,14,15,16,17]. In these works, together with de Sitter groups, several groups are considered as well as different starting actions that encodes gravity as a limit.…”