2,558 research outputs found
Complex Entangling Surfaces for AdS and Lifshitz Black Holes?
We discuss the possible relevance of complex codimension-two extremal
surfaces to the the Ryu-Takayanagi holographic entanglement proposal and its
covariant Hubeny-Rangamani-Takayanagi (HRT) generalization. Such surfaces live
in a complexified bulk spacetime defined by analytic continuation. We identify
surfaces of this type for BTZ, Schwarzschild-AdS, and Schwarzschild-Lifshitz
planar black holes. Since the dual CFT interpretation for the imaginary part of
their areas is unclear, we focus on a straw man proposal relating CFT entropy
to the real part of the area alone. For Schwarzschild-AdS and
Schwarzschild-Lifshitz, we identify families where the real part of the area
agrees with qualitative physical expectations for the appropriate CFT entropy
and, in addition, where it is smaller than the area of corresponding real
extremal surfaces. It is thus plausible that the CFT entropy is controlled by
these complex extremal surfaces.Comment: 28+5 pages. v2: Addressed referee comment
On Holographic Insulators and Supersolids
We obtain holographic realizations for systems that have strong similarities
to Mott insulators and supersolids, after examining the ground states of
Einstein-Maxwell-scalar systems. The real part of the AC conductivity has a
hard gap and a discrete spectrum only. We add momentum dissipation to resolve
the delta function in the conductivity due to translational invariance. We
develop tools to directly calculate the Drude weight for a large class of
solutions and to support our claims. Numerical RG flows are also constructed to
verify that such saddle points are IR fixed points of asymptotically AdS_4
geometries.Comment: 52 pages, jheppub, 15 figures; v2: minor corrections, references
adde
Comments on Holographic Entanglement Entropy and RG Flows
Using holographic entanglement entropy for strip geometry, we construct a
candidate for a c-function in arbitrary dimensions. For holographic theories
dual to Einstein gravity, this c-function is shown to decrease monotonically
along RG flows. A sufficient condition required for this monotonic flow is that
the stress tensor of the matter fields driving the holographic RG flow must
satisfy the null energy condition over the holographic surface used to
calculate the entanglement entropy. In the case where the bulk theory is
described by Gauss-Bonnet gravity, the latter condition alone is not sufficient
to establish the monotonic flow of the c-function. We also observe that for
certain holographic RG flows, the entanglement entropy undergoes a 'phase
transition' as the size of the system grows and as a result, evolution of the
c-function may exhibit a discontinuous drop.Comment: References adde
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
The Tachyon Potential in the Sliver Frame
We evaluate the tachyon potential in the Schnabl gauge through off-shell
computations in the sliver frame. As an application of the results of our
computations, we provide a strong evidence that Schnabl's analytic solution for
tachyon condensation in open string field theory represents a saddle point
configuration of the full tachyon potential. Additionally we verify that
Schnabl's analytic solution lies on the minimum of the effective tachyon
potential.Comment: v1: 19 pages, 1 figure, 1 table; v2: 20 pages, 1 figure, 2 tables, 1
reference added, comments added; v3: 21 pages, 1 figure, 2 tables, 4
references added, comments adde
An introduction to the study of critical points of solutions of elliptic and parabolic equations
We give a survey at an introductory level of old and recent results in the
study of critical points of solutions of elliptic and parabolic partial
differential equations. To keep the presentation simple, we mainly consider
four exemplary boundary value problems: the Dirichlet problem for the Laplace's
equation; the torsional creep problem; the case of Dirichlet eigenfunctions for
the Laplace's equation; the initial-boundary value problem for the heat
equation. We shall mostly address three issues: the estimation of the local
size of the critical set; the dependence of the number of critical points on
the boundary values and the geometry of the domain; the location of critical
points in the domain.Comment: 34 pages, 13 figures; a few slight changes and some references added;
to appear in the special issue, in honor of G. Alessandrini's 60th birthday,
of the Rendiconti dell'Istituto Matematico dell'Universit\`a di Triest
Non-Einstein geometries in Chiral Gravity
We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves.Comment: 11 pages, 3 figures. v2: references and comments on linear stability
(Sect.2) adde
A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors
We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying
the null energy condition and having two asymptotically AdS boundaries
connected through a (non-traversable) inflating wormhole. As for other
wormholes, it is natural to expect dual descriptions in terms of two
disconnected CFTs in appropriate entangled states. But for our cases certain
expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT)
prescription to compute CFT entropy do not exist. In particular, no real
codimension-2 extremal surface can run from one end of the wormhole to the
other. According to HRT, the mutual information between any two finite-sized
subregions (one in each CFT) must then vanish at leading order in large --
though the leading-order mutual information per unit area between the two CFTs
taken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have
plane-symmetric surfaces that would compute the total entropy of either CFT. We
suggest this to remain true of less-symmetric surfaces so that the HRT entropy
is ill-defined and some modified prescription is required. It may be possible
to simply extend HRT or the closely-related maximin construction by a limiting
procedure, though complex extremal surfaces could also play an important role.Comment: 27+10 pages. v2: minor modifications to address referee comments. v3:
fixed typo
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