Abstract

The interaction between Chern-Simons (CS) theories and localized external sources (2p-branes) is analyzed. This interaction generalizes the minimal coupling between a point charge (0-brane) and a gauge connection. The external currents that define the 2p branes are covariantly constant (D-2p-1)-forms coupled to (2p-1) CS forms. 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. In any dimension, 0-branes are constructed as topological defects produced by a surface deficit of (D-2)-sphere in anti-de Sitter space, and they are not constant curvature spaces for D>3. They correspond to dimensionally continued black holes with negative mass. On the other hand, in the case of CS (super) gravities, the (D-3)-branes are naked conical singularities (topological defects) obtained by identification of points with a Killing vector. In 2+1 dimensions, extremal spinning branes of this type are Bogomol'nyi-Prasad-Sommerfield states. Stable (D-3)-branes are shown to exist also in higher dimensions, as well. Classical field equations are also discussed, and in the presence of sources there is a large number of inequivalent and disconnected sectors in solution space. © 2009 The American Physical Society.