15 research outputs found
Higher Loop Nonplanar Anomalous Dimensions from Symmetry
In this article we study the action of the one loop dilatation operator on
operators with a classical dimension of order N. These operators belong to the
su(2) sector and are constructed using two complex fields Y and Z. For these
operators non-planar diagrams contribute already at the leading order in N and
the planar and large N limits are distinct. The action of the one loop and the
two loop dilatation operator reduces to a set of decoupled oscillators and
factorizes into an action on the Z fields and an action on the Y fields. Direct
computation has shown that the action on the Y fields is the same at one and
two loops. In this article, using the su(2) symmetry algebra as well as
structural features of field theory, we give compelling evidence that the
factor in the dilatation operator that acts on the Ys is given by the one loop
expression, at any loop order.Comment: 1+40 page
What is the dual of a dipole?
We study gravitational solutions that admit a dual CFT description and carry
non zero dipole charge. We focus on the black ring solution in AdS_3 x S^3 and
extract from it the one-point functions of all CFT operators dual to scalar
excitations of the six-dimensional metric. In the case of small black rings,
characterized by the level N, angular momentum J and dipole charge q_3, we show
how the large N and J dependence of the one-point functions can be reproduced,
under certain assumptions, directly from a suitable ensemble in the dual CFT.
Finally we present a simple toy model that describes the thermodynamics of the
small black ring for arbitrary values of the dipole charge.Comment: 34 page
Black Hole Bound States in AdS(3) x S**2
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 S1 × CY3 compactifications of M-theory. This includes a large number of multicentered black hole bound states asymptotic to AdS3 × S2. In addition, we find many geometries that develop multiple, mutually decoupled AdS3 × S2 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 S2, 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.Physic
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
A Universal Behavior of Half BPS Probes in the Superstar Ensemble
In this paper we probe the typical states of the superstar ensemble of
(hep-th/0508023) using half-BPS states of type-IIB string theory on AdS S. We find a very simple universal result that has the structure
\log\, \lag\lag \y \; \y \rag\rag_\calo \approx \a\, h \, \log N, where
is the conformal weight of the probe \y and \a is a constant that depends
mainly of the shape of the probe \y. A complete understanding of some
properties of this leading term from the dual effective superstar geometry
point of view is still lacking.Comment: 34 pages + appendice
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
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