1,127 research outputs found
Black Strings, Black Rings and State-space Manifold
State-space geometry is considered, for diverse three and four parameter
non-spherical horizon rotating black brane configurations, in string theory and
-theory. We have explicitly examined the case of unit Kaluza-Klein momentum
black strings, circular strings, small black rings and black
supertubes. An investigation of the state-space pair correlation functions
shows that there exist two classes of brane statistical configurations, {\it
viz.}, the first category divulges a degenerate intrinsic equilibrium basis,
while the second yields a non-degenerate, curved, intrinsic Riemannian
geometry. Specifically, the solutions with finitely many branes expose that the
two charged rotating black strings and three charged rotating small
black rings consort real degenerate state-space manifolds. Interestingly,
arbitrary valued -dipole charged rotating circular strings and Maldacena
Strominger Witten black rings exhibit non-degenerate, positively curved,
comprehensively regular state-space configurations. Furthermore, the
state-space geometry of single bubbled rings admits a well-defined, positive
definite, everywhere regular and curved intrinsic Riemannian manifold; except
for the two finite values of conserved electric charge. We also discuss the
implication and potential significance of this work for the physics of black
holes in string theory.Comment: 41 pages, Keywords: Rotating Black Branes; Microscopic
Configurations; State-space Geometry, PACS numbers: 04.70.-s Physics of black
holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black
holes, evaporation, thermodynamic
A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects
In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge
group U(N), compactified on S^3 in four dimensions using Monte-Carlo
techniques. The simulation is based on a particular reduction of degrees of
freedom to commuting matrices of constant fields, and in particular, we can
write the wave functions of these degrees of freedom exactly. The square of the
wave function is equivalent to a probability density for a Boltzman gas of
interacting particles in six dimensions. From the simulation we can extract the
density particle distribution for each wave function, and this distribution can
be interpreted as a special geometric locus in the gravitational dual. Studying
the wave functions associated to half-BPS giant gravitons, we are able to show
that the matrix model can measure the Planck scale directly. We also show that
the output of our simulation seems to match various theoretical expectations in
the large N limit and that it captures 1/N effects as statistical fluctuations
of the Boltzman gas with the expected scaling. Our results suggest that this is
a very promising approach to explore quantum corrections and effects in
gravitational physics on AdS spaces.Comment: 40 pages, 7 figures, uses JHEP. v2: references adde
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
- …