Stable p-branes in Chern-Simons AdS supergravities

TL;DR

This paper constructs and analyzes static p-brane solutions in odd-dimensional Chern-Simons AdS supergravity, exploring their stability, supersymmetry preservation, and explicit charged BPS states across various dimensions.

Contribution

It provides explicit static p-brane solutions in odd dimensions, examines their stability and supersymmetry, and identifies conditions for BPS states in Chern-Simons AdS supergravity.

Findings

3D 0-branes are negative mass BTZ black holes.

Stable 2-branes with electromagnetic charge exist in 5D for N≠4.

Certain 2-branes are BPS states with energy bounded from below.

Abstract

We construct static codimension-two branes in any odd dimension D, with negative cosmological constant, and show that they are exact solutions of Chern-Simons (super)gravity theory for (super)AdS coupled to external sources. The stability of these solutions is analyzed by counting the number of preserved supersymmetries. It is shown that static massive (D-3)-branes are unstable unless some suitable gauge fields are added and the brane is extremal. In particular, in three dimensions, a 0-brane is recognized as the negative mass counterpart of the BTZ black hole. For these 0-branes, we write explicitly electromagnetically charged BPS states with various number of preserved supersymmetries within the OSp(p|2) x OSp(q|2) supergroups. In five dimensions, we prove that stable 2-branes with electromagnetic charge always exist for the generic supergroup SU(2,2|N), where N is different than 4. For the special case N=4, in which the CS supergravity requires the addition of a nontrivial gauge field configuration in order to preserve maximal number of degrees of freedom, we show for two different static 2-branes that they are BPS states (one of which is the ground state), and from the corresponding algebra of charges we show that the energy is bounded from below. In higher dimensions, our results admit a straightforward generalization, although there are presumably more solutions corresponding to different intersections of the elementary objects.