CordonierTello, Fabrizio; Izaurieta, Fernando; Mella, Patricio; Rodríguez, Eduardo
(2016):
RandallSundrum brane Universe as a ground state for ChernSimons gravity.
In: Classical and Quantum Gravity, Vol. 33, No. 23, 235004

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Abstract
In stark contrast with the threedimensional case, higherdimensional ChernSimons (CS) theories can have nontopological, propagating degrees of freedom. Finding those vacua that allow for the propagation of linear perturbations, however, proves to be surprisingly challenging. The simplest solutions are somehow 'hyperstable', preventing the construction of realistic, fourdimensional physical models. Here, we show that a RandallSundrum (RS) brane Universe can be regarded as a vacuum solution of CS gravity in fivedimensional spacetime, with non vanishing torsion along the dimension perpendicular to the brane. Linearized perturbations around this solution not only exist, but behave as standard gravitational waves on a fourdimensional Minkowski background. In the nonperturbative regime, the solution leads to a fourdimensional 'cosmological function' Lambda(x) which depends on the Euler density of the brane. Interestingly, the fact that the solution admits nontrivial linear perturbations seems to be related to an often neglected property of the RS spacetime: that it is a group manifold, or, more precisely, two identical group manifolds glued together along the brane. The gravitational theory is then built around this fact, adding the Lorentz generators and one scalar generator needed to close the algebra. In this way, a conjecture emerges: a spacetime that is also a group manifold can be regarded as the ground state of a CS theory for an appropriate Lie algebra.