Naked Singularities, Topological Defects and Brane Couplings

TL;DR

This paper explores the relationship between topological defects like conical singularities in anti-de Sitter space and their associated coupling terms, extending the concept to higher-dimensional branes and gauge theories.

Contribution

It establishes a connection between the geometric identification of topological defects and the action coupling terms, generalizing to higher dimensions and various gauge theories.

Findings

Conical defects in (2+1) AdS space are point particles with delta-like singularities.

A coupling term in the action accounts for the source of the topological defect.

Extension of the coupling concept to higher-dimensional branes and gauge theories.

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 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.