19,852 research outputs found
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
Holographic R\'enyi Entropy and Generalized Entropy method
In this paper we use the method of generalized gravitational entropy in
\cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical
entangling surface, and calculate the R\'enyi entropy with the dual bulk
gravity theory being either Einstein gravity or Lovelock gravity, this approach
is closely related to that in \cite{Casini:2011kv}. For a general entangling
surface we derive the area law of entanglement entropy. The area law is closely
related with the local property of the entangling surface.Comment: 17+6 page
Conformal Correlation Functions, Frobenius Algebras and Triangulations
We formulate two-dimensional rational conformal field theory as a natural
generalization of two-dimensional lattice topological field theory. To this end
we lift various structures from complex vector spaces to modular tensor
categories. The central ingredient is a special Frobenius algebra object A in
the modular category that encodes the Moore-Seiberg data of the underlying
chiral CFT. Just like for lattice TFTs, this algebra is itself not an
observable quantity. Rather, Morita equivalent algebras give rise to equivalent
theories. Morita equivalence also allows for a simple understanding of
T-duality.
We present a construction of correlators, based on a triangulation of the
world sheet, that generalizes the one in lattice TFTs. These correlators are
modular invariant and satisfy factorization rules. The construction works for
arbitrary orientable world sheets, in particular for surfaces with boundary.
Boundary conditions correspond to representations of the algebra A. The
partition functions on the torus and on the annulus provide modular invariants
and NIM-reps of the fusion rules, respectively.Comment: 17 pages, LaTeX2e; v2: more references and Note added in proo
Quivers, Tilings, Branes and Rhombi
We describe a simple algorithm that computes the recently discovered brane
tilings for a given generic toric singular Calabi-Yau threefold. This therefore
gives AdS/CFT dual quiver gauge theories for D3-branes probing the given
non-compact manifold. The algorithm solves a longstanding problem by computing
superpotentials for these theories directly from the toric diagram of the
singularity. We study the parameter space of a-maximization; this study is made
possible by identifying the R-charges of bifundamental fields as angles in the
brane tiling. We also study Seiberg duality from a new perspective.Comment: 36 pages, 40 figures, JHEP
4d /2d Yang-Mills Duality in Holography
We study the supergravity dual of four-dimensional
superconformal field theories arising from wrapping M5-branes on a K\"ahler
two-cycle inside a Calabi-Yau threefold. We derive an effective
three-dimensional theory living on the cobordism between the infrared and
ultraviolet Riemann surfaces, describing the renormalization group flows
between AdS and AdS as well as between different AdS fixed
points. The realization of this system as an effective theory is convenient to
make connections to known theories, and we show that upon imposing (physical)
infrared boundary conditions, the effective three-dimensional theory further
reduces to two-dimensional Yang-Mills theory on the Riemann surface,
thus deriving a correspondence between the gravity duals of a class of
superconformal field theories arising from wrapping M5-branes
on a Riemann surface and two-dimensional Yang-Mills theory on the same Riemann
surface.Comment: 18 pages, 2 figure
Membranes with Topological Charge and AdS4/CFT3 Correspondence
If the second Betti number b_2 of a Sasaki-Einstein manifold Y^7 does not
vanish, then M-theory on AdS_4 x Y^7 possesses "topological" U(1)^{b_2} gauge
symmetry. The corresponding Abelian gauge fields come from three-form
fluctuations with one index in AdS_4 and the other two in Y^7. We find black
membrane solutions carrying one of these U(1) charges. In the zero temperature
limit, our solutions interpolate between AdS_4 x Y^7 in the UV and AdS_2 x R^2
x squashed Y^7 in the IR. In fact, the AdS_2 x R^2 x squashed Y^7 background is
by itself a solution of the supergravity equations of motion. These solutions
do not appear to preserve any supersymmetry. We search for their possible
instabilities and do not find any. We also discuss the meaning of our charged
membrane backgrounds in a dual quiver Chern-Simons gauge theory with a global
U(1) charge density. Finally, we present a simple analytic solution which has
the same IR but different UV behavior. We reduce this solution to type IIA
string theory, and perform T-duality to type IIB. The type IIB metric turns out
to be a product of the squashed Y^7 and the extremal BTZ black hole. We discuss
an interpretation of this type IIB background in terms of the (1+1)-dimensional
CFT on D3-branes partially wrapped over the squashed Y^7.Comment: 57 pages, 7 figure
Finite, diffeomorphism invariant observables in quantum gravity
Two sets of spatially diffeomorphism invariant operators are constructed in
the loop representation formulation of quantum gravity. This is done by
coupling general relativity to an anti- symmetric tensor gauge field and using
that field to pick out sets of surfaces, with boundaries, in the spatial three
manifold. The two sets of observables then measure the areas of these surfaces
and the Wilson loops for the self-dual connection around their boundaries. The
operators that represent these observables are finite and background
independent when constructed through a proper regularization procedure.
Furthermore, the spectra of the area operators are discrete so that the
possible values that one can obtain by a measurement of the area of a physical
surface in quantum gravity are valued in a discrete set that includes integral
multiples of half the Planck area. These results make possible the construction
of a correspondence between any three geometry whose curvature is small in
Planck units and a diffeomorphism invariant state of the gravitational and
matter fields. This correspondence relies on the approximation of the classical
geometry by a piecewise flat Regge manifold, which is then put in
correspondence with a diffeomorphism invariant state of the gravity-matter
system in which the matter fields specify the faces of the triangulation and
the gravitational field is in an eigenstate of the operators that measure their
areas.Comment: Latex, no figures, 30 pages, SU-GP-93/1-
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