25 research outputs found
Holographic confinement in inhomogenous backgrounds
As noted by Witten, compactifying a -dimensional holographic CFT on an
gives a class of -dimensional confining theories with gravity
duals. The prototypical bulk solution dual to the ground state is a double Wick
rotation of the AdS Schwarzschild black hole known as the AdS soliton.
We generalize such examples by allowing slow variations in the size of the
, and thus in the confinement scale. Coefficients governing the second
order response of the system are computed for using a
derivative expansion closely related to the fluid-gravity correspondence. The
primary physical results are that i) gauge-theory flux tubes tend to align
orthogonal to gradients and along the eigenvector of the Hessian with the
lowest eigenvalue, ii) flux tubes aligned orthogonal to gradients are attracted
to gradients for but repelled by gradients for , iii) flux
tubes are repelled by regions where the second derivative along the tube is
large and positive but are attracted to regions where the eigenvalues of the
Hessian are large and positive in directions orthogonal to the tube, and iv)
for , inhomogeneities act to raise the total energy of the confining
vacuum above its zeroth order value.Comment: 16 pages, 6 figures, typos correcte
The Torus Operator in Holography
We consider the non-local operator defined in 2-dimensional
CFTs by the path integral over a torus with two punctures. Using the AdS/CFT
correspondence, we study the spectrum and ground state of this operator in
holographic such CFTs in the limit of large central charge . In one region
of moduli space, we argue that the operator retains a finite gap and has a
ground state that differs from the CFT vacuum only by order one corrections. In
this region the torus operator is much like the cylinder operator. But in
another region of moduli space we find a puzzle. Although our is
of the manifestly positive form , studying the most tractable
phases of suggests that has
negative eigenvalues. It seems clear that additional phases must become
relevant at large , perhaps leading to novel behavior associated with a
radically different ground state or a much higher density of states. By
studying the action of two such torus operators on the CFT ground state, we
also provide evidence that, even at large , the relevant bulk saddles have
surfaces with small genus.Comment: 42 pages, 24 figures, introduction rewritten for clarity, appendix
adde
Adiabatic corrections to holographic entanglement in thermofield doubles and confining ground states
We study entanglement in states of holographic CFTs defined by Euclidean path
integrals over geometries with slowly varying metrics. In particular, our CFT
spacetimes have fibers whose size varies along one direction () of
an base. Such examples respect an
Euclidean symmetry. Treating the direction as time leads to a thermofield
double state on a spacetime with adiabatically varying redshift, while treating
another direction as time leads to a confining ground state with slowly varying
confinement scale. In both contexts the entropy of slab-shaped regions defined
by exhibits well-known phase transitions at length scales characterizing the CFT entanglements. For the thermofield double, the
numerical coefficients governing the effect of variations in on the
transition are surprisingly small and exhibit an interesting change of sign:
gradients reduce for but increase for .
This means that, while for general they significantly increase
the mutual information of opposing slabs as one would expect, for
gradients cause a small decrease near the phase transition. In contrast, for
the confining ground states gradients always decrease , with the
effect becoming more pronounced in higher dimensions.Comment: 32 pages, 16 figures, typos fixed and reg. procedure refine
Handlebody phases and the polyhedrality of the holographic entropy cone
The notion of a holographic entropy cone has recently been introduced and it
has been proven that this cone is polyhedral. However, the original definition
was fully geometric and did not strictly require a holographic duality. We
introduce a new definition of the cone, insisting that the geometries used for
its construction should be dual to states of a CFT. As a result, the
polyhedrality of this holographic cone does not immediately follow. A numerical
evaluation of the Euclidean action for the geometries that realize extremal
rays of the original cone indicates that these are subdominant bulk phases of
natural path integrals. The result challenges the expectation that such
geometries are in fact dual to CFT states.Comment: 20 pages, 7 figures, minor change, added ref, published versio
Holographic Holes and Differential Entropy
Recently, it has been shown by Balasubramanian et al. and Myers et al. that
the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in
the bulk of a holographic spacetime has an interpretation as the differential
entropy of a particular family of intervals (or strips) in the boundary theory.
We first extend this construction to bulk surfaces which vary in time. We then
give a general proof of the equality between the gravitational entropy and the
differential entropy. This proof applies to a broad class of holographic
backgrounds possessing a generalized planar symmetry and to certain classes of
higher-curvature theories of gravity. To apply this theorem, one can begin with
a bulk surface and determine the appropriate family of boundary intervals by
considering extremal surfaces tangent to the given surface in the bulk.
Alternatively, one can begin with a family of boundary intervals; as we show,
the differential entropy then equals the gravitational entropy of a bulk
surface that emerges from the intersection of the neighboring entanglement
wedges, in a continuum limit.Comment: 62 pages; v2: minor improvements to presentation, references adde
Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic
quantum error-correcting code to provide a toy model for bulk gauge fields or
linearized gravitons. The key new elements are the introduction of degrees of
freedom on the links (edges) of the associated tensor network and their
connection to further copies of the HaPPY code by an appropriate isometry. The
result is a model in which boundary regions allow the reconstruction of bulk
algebras with central elements living on the interior edges of the (greedy)
entanglement wedge, and where these central elements can also be reconstructed
from complementary boundary regions. In addition, the entropy of boundary
regions receives both Ryu-Takayanagi-like contributions and further corrections
that model the term of Faulkner, Lewkowycz,
and Maldacena. Comparison with Yang-Mills theory then suggests that this
term can be reinterpreted as a part of the
bulk entropy of gravitons under an appropriate extension of the physical bulk
Hilbert space.Comment: 20 pages, 11 figure
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Black Holes and Holography: Insights and Applications
This dissertation focuses on the role classical black hole spacetimes play in the AdS/CFT correspondence. We begin by introducing some of the puzzles surrounding black holes, and we review their connection to strongly correlated CFT states through holography. Additionally, we detail numerical methods for constructing black hole states of non-trivial topology in three dimensions and evaluating their actions.In part I we focus on using black hole spacetimes to derive insights into holography and quantum gravity. Using numerical methods, we study a class of non-local operators in the CFT, defined via a path integral over a torus with two punctures. In particular, we are interested in determining the spectrum of such operators at various points in moduli space. In the dual gravitational theory, such an operator might be used to construct black hole spacetimes with arbitrarily high topology behind the horizon. We present evidence suggesting this fails, and along the way encounter a puzzle related to the positivity of these operators. The resolution of this puzzle lies in developing technology to better catalogue the relevant gravitational phases.Additionally, we use multi-boundary wormhole spacetimes to investigate the constraints on the subregion entanglement entropies of holographic states. We find tension with previously claimed properties of these constraints, namely that they define a polyhedral cone in the space of entanglement entropies. These results either suggest the possible existence of further unknown constraints, or the need for a more complicated construction procedure to realize the extremal states.In part II we focus on the holographic description of CFT states via black hole spacetimes, focusing on spacetimes perturbatively constructed from the planar AdS-Schwarzschild metric. First, we consider corrections to properties of confining ground states of holographic CFTs as we introduce spatial curvature. Next, we compute shifts in vacuum entanglement entropy in a thermal state with a locally varying temperature as well as similar shifts in the confining ground states with spatial curvature