Supersymmetric black holes in 2D dilaton supergravity: baldness and extremality

Abstract

We present a systematic discussion of supersymmetric solutions of 2D dilaton supergravity. In particular those solutions which retain at least half of the supersymmetries are ground states with respect to the bosonic Casimir function (essentially the ADM mass). Nevertheless, by tuning the prepotential appropriately, black hole solutions may emerge with an arbitrary number of Killing horizons. The absence of dilatino and gravitino hair is proven. Moreover, the impossibility of supersymmetric dS ground states and of nonextremal black holes is confirmed, even in the presence of a dilaton. In these derivations the knowledge of the general analytic solution of 2D dilaton supergravity plays an important rôle. The latter result is addressed in the more general context of gPSMs which have no supergravity interpretation.Finally it is demonstrated that the inclusion of non-minimally coupled matter, a step which is already nontrivial by itself, does not change these features in an essential way. * 4 Conventions and light cone coordinates are summarized in app. A. 5 CDV solutions with u = 0 must obey u ′ /u = − 1 2 Z, which leads to C S = 0 while C B = 0. Clearly, they cannot respect both supersymmetries.

Chemistry of Chern-Simons Supergravity: reduction to a BPS kink, oxidation to M-theory and thermodynamical aspects

“…We will treat only self dual fluxes explicitly but the anti-self dual ones may be obtained by exchanging + indices with − indices in all subsequent considerations. 22 That it is also sufficient in the present case can be checked easily by considering the restrictions on the SUSY transformation parameters ǫ± in sect. 4 of [22].…”

“…Although each of these properties alone is not sufficient to guarantee BPS, taken together they are. Technically, the crucial observation is that the conservation equation in presence of matter, (7.4) of [22], reduces to the one in the absence of matter because 1. no fermions are present, 2. the matter component X ++ W −− vanishes as the matter component W −− = 0 and 3. the remaining matter contribution X −− W ++ vanishes as well because W ++ = 0 is valid only on the horizon where X −− = 0. Thus, C = 0 is still the ground state which is necessary 22 for BPS states with vanishing fermions.…”

An action for the exact string black hole

“…Once the pre-potential is defined one may apply a standard machinery [56,57] to obtain the supersymmetry transformations and all classical solutions including the BPS states. Because it is not the purpose of the present work to review these techniques the focus is solely on the pre-potential.…”

Canonical exterior formalism on group manifold for (3+1) dimensional supergravity

“…Recently [19], the Bogomolnyi-Prasad-Sommerfield black holes were studied in the framework of the two-dimensional dilaton supergravity. This was done in the first order formalism by starting from the action for the graded Poisson-Sigma model.…”