NAKED SINGULARITIES, TOPOLOGICAL DEFECTS AND BRANE COUPLINGS
Abstract
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 δ-like singularity at the conical defect, but that does not 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 couples 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.
| You currently do not have access to the full text article. |
|---|
