N = 2 supergravity in four dimensions, or equivalently N = 1 supergravity in five dimensions, has an interesting set of BPS solutions that each correspond to a number of charged centers. This set contains black holes, black rings and their bound states, as well as many smooth solutions. Moduli spaces of such solutions carry a natural symplectic form which we determine, and which allows us to study their quantization. By counting the resulting wavefunctions we come to an independent derivation of some of the wallcrossing formulae. Knowledge of the explicit form of these wavefunctions allows us to find quantum resolutions to some apparent classical paradoxes such as solutions with barely bound centers and those with an infinitely deep throat. We show that quantum effects seem to cap off the throat at a finite depth and we give an estimate for the corresponding mass gap in the dual CFT. This is an interesting example of a system where quantum effects cannot be neglected at macroscopic scales even though the curvature is everywhere small. arXiv:0807.4556v1 [hep-th] 29 Jul 2008Note that the spacetime contribution (from the vertices) and the "internal" contributions (nodes) are easily and clearly separated in this computation. For more details, including a derivation (assuming the split attractor conjecture) the reader is referred to [23] and [15]. Simple Solution SpacesLet us describe some simple moduli spaces of solutions in order to have some feeling for the spaces we wish to quantize (in section 4). We begin with the simple case of the two centers solution and then discuss the three centers case. The Two Center CaseThe solution space for two centers, when it exists, is two dimensional. The constraint

The understanding of the fermionic sector of the worldvolume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory, like for example the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in absence of fluxes. A nonzero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.

We systematically construct the geometries dual to the 1+1 dimensional (0,4) conformal field theories that arise in the low-energy description of wrapped M5-branes in S 1 × CY 3 compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS 3 × S 2 . In addition, we find many geometries that develop multiple, mutually decoupled AdS 3 × S 2 throats. We argue there is a useful one to one correspondence between the connected components of the space of solutions and particular limits of type IIA attractor flow trees. We point out that there is a thermodynamic instability of small supersymmetric BTZ black holes to localization on the S 2 , a supersymmetric and exactly solvable analog of the well known AdS-Schwarzschild localization instability, and identify this with the "Entropy Enigma" in four dimensions. We discuss the phase transition this suggests, and initiate the CFT interpretation of these results.

We revisit the manifestly covariant large c expansion of General Relativity, c being the speed of light. Assuming the relativistic connection has no pole in c −2 , this expansion is known to reproduce Newton-Cartan gravity and a covariant version of Post-Newtonian corrections to it. We show that relaxing this assumption leads to the inclusion of twistless torsion in the effective non-relativistic theory. We argue that the resulting TTNC theory is an effective description of a non-relativistic regime of General Relativity that extends Newtonian physics by including strong gravitational time dilation.