2 00 9 Couplings between Chern - Simons gravities and 2 p - branes

The interaction between Chern-Simons (CS) theories and localized external sources (2pbranes) is analyzed. The generally covariant, gauge-invariant and background independent interactions generalize the minimal coupling between a point charge (0-brane) and a gauge connection. The branes define covariantly conserved external currents which couple to CS forms of the same dimension. The general expression for the sources, charged with respect to the corresponding gauge algebra is presented, focusing on two special cases: 0-branes and (D − 3)-branes. The classical field equations are discussed and it is shown that, besides the pure gauge configurations that are always generic classical solutions, there exist various other inequivalent and disconnected sectors in solution space. In the case of CS (super) gravities, the (D−3)-branes present naked conical singularities obtained as topological defects via identification of points by a Killing vector. It is shown that, apart from the massless (M = 0 = J) and extremal (M = −|J |/l) black holes in 2 + 1 dimensions, or the globally AdS (M = −1, J = 0) geometry, extremal spinning branes may be BPS states as well. On the other hand, 0-branes are constructed as topological defects arising due to surface deficit in the AdS space, and do not have constant curvature. These solutions are examples of consistent couplings between 2p-branes and nonabelian connections provided by CS forms.