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Item Lie-algebra expansions, Chern–Simons theories and the Einstein–Hilbert LagrangianAutores: Edelstein, J.D.; Hassaine, M.; Troncoso, R.; Zanelli, J.Starting from gravity as a Chern–Simons action for the AdS algebra in five dimensions, it is possible to modify the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein–Hilbert action plus non-minimally coupled matter. The modified system is gauge invariant under the Poincaré 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 non-minimal 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.Item Optical properties of a theta vacuumAutores: Huerta, L.; Zanelli, J.Chern-Simons (CS) forms generalize the minimal coupling between gauge potentials and point charges to sources represented by charged extended objects (branes). The simplest example of such a CS-brane coupling is a domain wall coupled to the electromagnetic CS three-form. This describes a topologically charged interface where the CS form A boolean AND dA is supported, separating two three-dimensional spatial regions in 3 + 1 spacetime. Electrodynamics at either side of the brane is described by the same Maxwell's equations, but those two regions have different vacua characterized by a different value of the theta-parameter multiplying the Pontryagin form F boolean AND F. The theta-term is the Abelian version of the concept introduced by 't Hooft for the resolution of the U(1) problem in QCD. We point out that CS-generalized classical electrodynamics show new phenomena when two neighboring regions with different theta-vacua are present. These topological effects result from surface effects induced by the boundary, and we explore the consequences of such boundary effects for the propagation of the electromagnetic field in Maxwell theory. Several features including optical and electrostatic/magnetostatic responses, which may be observable in condensed matter systems like topological insulators, are discussed.Item Supersymmetry of a different kindAutores: Alvarez, P.D.; Valenzuela, M.; Zanelli, J.A local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under local (gauge) supersymmetry. Although the supersymmetry is locally realized, there is no spin-3/2 gravitino, and is therefore not supergravity. The fields do not necessarily form supersymmetric doublets of equal mass, and moreover, the fermion may acquire mass through the coupling with geometry, while the bosons - the U(1) field and the spin connection - remain massless.
