Standard General Relativity from Chern-Simons theories in d = 5: an alternative procedure

por Nelson Merino (Instituto de Física Pontificia, Universidad Católica de Valparaiso - Chile)

martes 5 mar. 2013 12:00 → 13:00 Europe/Madrid

Sala Seminarios (Dpto. de Física Teórica (UVEG))

It was recently proposed a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point of a particular Chern-Simons (CS) action. To achieve this result, both the Lie algebra and the symmetric invariant tensor that define the CS Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite abelian semigroup. An interesting question that emerges is the following one: are there other Lie algebras that, constructed also by means of the S-expansion method, permits to construct a CS lagrangian that in a certain critical point also lead to standard General Relativity in d=5. To answer this question the general properties of the expansion method are studied. This permits to perform the S-expansion at the level of the CS Lagrangian (for the AdS algebra) with an arbitrary-unknown semigroup. Then we establish the conditions that the semigroup must satisfy in order to lead the desired connection to standard General Relativity. Finally we implement those conditions by means of computer programs which give us the solution. We propose this procedure as a useful tool in problems where it is important to find a physical theory or a family of them that, on a certain limit, converge to some particular theory. For example, to study if a similar relation can be generalized to the supersymmetric case.