  A conical defect in (2+1) anti-de Sitter space is a BTZ solution with a
negative mass parameter. This is a naked singularity, but a rather harmless
one: it is a point particle. Naturally, the energy density and the spacetime
curvature have a delta-like singularity at the apex of the conical defect, but
that doesn't give rise to any unphysical situations. Since the conical solution
implies the presence of a source, applying reverse enginnering, one can
identify the coupling term that is required in the action to account for that
source. In that way, a relation is established between the identification
operation that gives rise to the topological defect and the interaction term in
the action that produces it. This idea has a natural extension to higher
dimensions, where instead of a point particle (zero-brane) one finds membranes
of even spatial dimensions (p-branes, with p=2n). The generalization to other
abelian and nonabelian gauge theories --including (super-) gravities-- is
fairly straightforward: the 2n-brane couple to a (2n+1) Chern-Simons form. The
construction suggests a generic role for Chern-Simons forms as the natural way
to couple a gauge connection to a brane and avoids the inconsistency that
results from the minimal coupling between a brane and a fundamental p-form
field.
