Stablep-branes in Chern-Simons AdS supergravities

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 D 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 magnetically charged BPS states with various number of preserved supersymmetries within the OSp(p|2) × OSp(q|2) supergroups. In five dimensions, we prove that stable 2-branes with magnetic charge always exist for the generic supergroup SU (2, 2|N ), where N = 4. For the special case N = 4, in which 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.

Optical properties of aθvacuum

“…Couplings of this sort have been considered in the past in various settings, including supergravity [12], in 2+1 AdS gravity [13], and higher dimensions [14,15,16,17]. In our fourdimensional spacetime there are two types of branes that can be coupled in this manner: 0-branes (point particles) and 2-branes (ordinary two-dimensional surfaces evolving in spacetime).…”

Geometry and stability of spinning branes in AdS gravity

“…[23], because both cases (spinning and static) have locally the same form. Thus, in the background of an uncharged 0-brane and with a suitable representation of the generators, the Killing spinor equation for each copy of OSp(p|2) has the form…”

“…The identification by ξ 1 produces a static 2-brane in the x 1 -x 2 -plane [23], and ξ 2 boosts it in the perpendicular direction producing a spinning 2-brane if b 2 = 0 (see Section 2). The corresponding norms are…”

“…For a static 2-brane, there is only one nontrivial parameter, which is not an integer. Hence the extremality conditions (3.83) cannot be fulfilled -the static 2-brane without bosonic CS matter is not stable [23]. If there is a nonvaninshing angular momentum, then two or more parameters are not integers, and the extremality conditions (3.83) could in principle be satisfied by a one-parameter family of configurations.…”

“…Because some azimuthal angles have deficits with respect to global AdS, conical singularities are generated in the submanifolds that coincide with worldvolumes of static branes, and also causal horizons are generated when the branes are rotating. For example, if only the angle φ 12 has a deficit 2π(1 − a 0 ), and other angles φ 2i+1,2i+2 have period 2π, a static 2p-brane is produced with conical singularity at the origin, B = 0; the deficit a 0 is related to the negative mass parameter of the brane M [23].…”