3 research outputs found
A bound on the entropy of supergravity?
We determine, in two independent ways, the number of BPS quantum states
arising from supergravity degrees of freedom in a system with fixed total D4D0
charge. First, we count states generated by quantizing the spacetime degrees of
freedom of 'entropyless' multicentered solutions consisting of anti-D0-branes
bound to a D6-anti-D6 pair. Second, we determine the number of free
supergravity excitations of the corresponding AdS_3 geometry with the same
total charge. We find that, although these two approaches yield a priori
different sets of states, the leading degeneracies in a large charge expansion
are equal to each other and that, furthermore, the number of such states is
parametrically smaller than that arising from the D4D0 black hole's entropy.
This strongly suggests that supergravity alone is not sufficient to capture all
degrees of freedom of large supersymmetric black holes. Comparing the free
supergravity calculation to that of the D6-anti-D6-D0 system we find that the
bound on the free spectrum imposed by the stringy exclusion principle (a
unitarity bound in the dual CFT) seems to be captured in the dynamics of the
fully interacting but classcial supergravity equations of motion.Comment: 33 pages, 5 figure
Black Holes as Effective Geometries
Gravitational entropy arises in string theory via coarse graining over an
underlying space of microstates. In this review we would like to address the
question of how the classical black hole geometry itself arises as an effective
or approximate description of a pure state, in a closed string theory, which
semiclassical observers are unable to distinguish from the "naive" geometry. In
cases with enough supersymmetry it has been possible to explicitly construct
these microstates in spacetime, and understand how coarse-graining of
non-singular, horizon-free objects can lead to an effective description as an
extremal black hole. We discuss how these results arise for examples in Type II
string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8
supercharges respectively. For such a picture of black holes as effective
geometries to extend to cases with finite horizon area the scale of quantum
effects in gravity would have to extend well beyond the vicinity of the
singularities in the effective theory. By studying examples in M-theory on
AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.Comment: Review based on lectures of JdB at CERN RTN Winter School and of VB
at PIMS Summer School. 68 pages. Added reference
Quantizing N=2 Multicenter Solutions
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 wall-crossing 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.Comment: 49 pages + appendice