  Starting from gravity as a Chern-Simons action for the AdS algebra in five
dimensions, it is possible to deform the theory through an expansion of the Lie
algebra that leads to a system consisting of the Einstein-Hilbert action plus
nonminimally coupled matter. The deformed system is gauge invariant under the
Poincare group enlarged by an Abelian ideal. Although the resulting action
naively looks like General Relativity plus corrections due to matter sources,
it is shown that the nonminimal couplings produce a radical departure from GR.
Indeed, the dynamics is not continuously connected to the one obtained from
Einstein-Hilbert action. In a matter-free configuration and in the torsionless
sector, the field equations are too strong a restriction on the geometry as the
metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In
particular, the five-dimensional Schwarzschild geometry fails to be a solution;
however, configurations corresponding to a brane-world with positive
cosmological constant on the worldsheet are admissible when one of the matter
fields is switched on. These results can be extended to higher odd dimensions.

High Energy Physics - Theory