Couplings between Chern-Simons gravities and 2p-branes

TL;DR

This paper explores the interaction between Chern-Simons gravities and 2p-branes, revealing how these topological defects relate to black holes, conical singularities, and BPS states across various dimensions.

Contribution

It provides a general framework for coupling 2p-branes to Chern-Simons theories, including explicit solutions and the classification of topological defects in diverse dimensions.

Findings

0-branes are topological defects with negative mass in AdS space.

(D-3)-branes are conical singularities obtained by point identification.

Stable higher-dimensional branes and BPS states are identified.

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 AdS 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 BPS 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.