2,014 research outputs found
Bare Quantum Null Energy Condition
The quantum null energy condition (QNEC) is a conjectured relation between a
null version of quantum field theory energy and derivatives of quantum field
theory von Neumann entropy. In some cases, divergences cancel between these two
terms and the QNEC is intrinsically finite. We study the more general case here
where they do not and argue that a QNEC can still hold for bare
(unrenormalized) quantities. While the original QNEC applied only to locally
stationary null congruences in backgrounds that solve semiclassical theories of
quantum gravity, at least in the formal perturbation theory at a small Planck
length, the quantum focusing conjecture can be viewed as the special case of
our bare QNEC for which the metric is on shell.Comment: 5 pages, no figure; v2: minor corrections; v3: modifications to
address referee comments; v4: title and abstract change
Does horizon entropy satisfy a Quantum Null Energy Conjecture?
A modern version of the idea that the area of event horizons gives times
an entropy is the Hubeny-Rangamani Causal Holographic Information (CHI)
proposal for holographic field theories. Given a region of a holographic
QFTs, CHI computes on a certain cut of an event horizon in the
gravitational dual. The result is naturally interpreted as a coarse-grained
entropy for the QFT. CHI is known to be finitely greater than the fine-grained
Hubeny-Rangamani-Takayanagi (HRT) entropy when lies on a Killing
horizon of the QFT spacetime, and in this context satisfies other non-trivial
properties expected of an entropy. Here we present evidence that it also
satisfies the quantum null energy condition (QNEC), which bounds the second
derivative of the entropy of a quantum field theory on one side of a
non-expanding null surface by the flux of stress-energy across the surface. In
particular, we show CHI to satisfy the QNEC in 1+1 holographic CFTs when
evaluated in states dual to conical defects in AdS. This surprising result
further supports the idea that CHI defines a useful notion of coarse-grained
holographic entropy, and suggests unprecedented bounds on the rate at which
bulk horizon generators emerge from a caustic. To supplement our motivation, we
include an appendix deriving a corresponding coarse-grained generalized second
law for 1+1 holographic CFTs perturbatively coupled to dilaton gravity.Comment: 29 pages, 5 figures; v2: minor corrections; v3: 30 pages, 6 figures,
modifications to address referee comments, one figure adde
Violating the Quantum Focusing Conjecture and Quantum Covariant Entropy Bound in dimensions
We study the Quantum Focussing Conjecture (QFC) in curved spacetime. Noting
that quantum corrections from integrating out massive fields generally induce a
Gauss-Bonnet term, we study Einstein-Hilbert-Gauss-Bonnet gravity and show for
spacetime dimensions that weakly-curved solutions can violate the
associated QFC for either sign of the Gauss-Bonnet coupling. The nature of the
violation shows that -- so long as the Gauss-Bonnet coupling is non-zero -- it
will continue to arise for local effective actions containing arbitrary further
higher curvature terms, and when gravity is coupled to generic
theories of massive quantum fields. The argument also implies violations of a
recently-conjectured form of the generalized covariant entropy bound. The
possible validity of the QFC and covariant entropy bound in spacetime
dimensions remains open.Comment: 13 pages, no figure; v2: note adde
A coarse-grained generalized second law for holographic conformal field theories
We consider the universal sector of a -dimensional large-
strongly-interacting holographic CFT on a black hole spacetime background .
When our CFT is coupled to dynamical Einstein-Hilbert gravity with Newton
constant , the combined system can be shown to satisfy a version of the
thermodynamic Generalized Second Law (GSL) at leading order in . The
quantity is
non-decreasing, where is the (time-dependent) area
of the new event horizon in the coupled theory. Our is the notion of
(coarse-grained) CFT entropy outside the black hole given by causal holographic
information -- a quantity in turn defined in the AdS dual by the
renormalized area of a corresponding bulk causal
horizon. A corollary is that the fine-grained GSL must hold for finite
processes taken as a whole, though local decreases of the fine-grained
generalized entropy are not obviously forbidden. Another corollary, given by
setting , states that no finite process taken as a whole can
increase the renormalized free energy , with constants set by . This latter corollary
constitutes a 2nd law for appropriate non-compact AdS event horizons.Comment: minor corrections, 18 page
The Quantum Null Energy Condition in Curved Space
The quantum null energy condition (QNEC) is a conjectured bound on components
) of the stress tensor along a null vector at a
point in terms of a second -derivative of the von Neumann entropy on
one side of a null congruence through generated by . The
conjecture has been established for super-renormalizeable field theories at
points that lie on a bifurcate Killing horizon with null tangent and
for large-N holographic theories on flat space. While the Koeller-Leichenauer
holographic argument clearly yields an inequality for general , more
conditions are generally required for this inequality to be a useful QNEC. For
, for arbitrary backgroud metric satisfying the null convergence
condition , we show that the QNEC is naturally finite and
independent of renormalization scheme when the expansion and shear
of at point satisfy ,
. This is consistent with the original QNEC conjecture. But
for more conditions are required. In particular, we also require the
vanishing of additional derivatives and a dominant energy condition. In the
above cases the holographic argument does indeed yield a finite QNEC, though
for we argue these properties to fail even for weakly isolated horizons
(where all derivatives of vanish) that also satisfy a
dominant energy condition. On the positive side, a corrollary to our work is
that, when coupled to Einstein-Hilbert gravity, holographic theories
at large satisfy the generalized second law (GSL) of thermodynamics at
leading order in Newton's constant . This is the first GSL proof which does
not require the quantum fields to be perturbations to a Killing horizon.Comment: 31 pages, no figure; v2: signs corrected and new comments for d=3;
v3: minor corrections; v4: minor modifications to address referee comments;
v5: paragraph containing equation (2.13) modifie
Causal holographic information does not satisfy the linearized quantum focusing condition
The Hubeny-Rangamani causal holographic information (CHI) defined by a region
of a holographic quantum field theory (QFT) is a modern version of the idea
that the area of event horizons might be related to an entropy. Here the event
horizon lives in a dual gravitational bulk theory with Newton's constant
, and the relation involves a factor of . The fact
that CHI is bounded below by the von Neumann entropy suggests that CHI is
coarse-grained. Its properties could thus differ markedly from those of . In
particular, recent results imply that when holographic QFTs are
perturbatively coupled to -dimensional gravity, the combined system
satisfies the so-called quantum focusing condition (QFC) at leading order in
the new gravitational coupling when the QFT entropy is taken to be that
of von Neumann. However, by studying states dual to spherical bulk (anti--de
Sitter) Schwarschild black holes in the conformal frame for which the boundary
is a -dimensional de Sitter space, we find the QFC defined by CHI is
violated even when perturbing about a Killing horizon and using a single null
congruence. Since it is known that a generalized second law (GSL) holds in this
context, our work demonstrates that the QFC is not required in order for an
entropy, or an entropy-like quantity, to satisfy such a GSL.Comment: 12 pages, 3 figures; v2: modifications to address referee comment
A perturbative perspective on self-supporting wormholes
We describe a class of wormholes that generically become traversable after
incorporating gravitational back-reaction from linear quantum fields satisfying
appropriate (periodic or anti-periodic) boundary conditions around a
non-contractible cycle, but with natural boundary conditions at infinity (i.e.,
without additional boundary interactions). The class includes both
asymptotically flat and asymptotically AdS examples. Simple asymptotically
AdS or asymptotically AdS examples with a single periodic
scalar field are then studied in detail. When the examples admit a smooth
extremal limit, our perturbative analysis indicates the back-reacted wormhole
remains traversable at later and later times as this limit is approached. This
suggests that a fully non-perturbative treatment would find a self-supporting
eternal traversable wormhole. While the general case remains to be analyzed in
detail, the likely relation of the above effect to other known instabilities of
extreme black holes may make the construction of eternal traversable wormholes
more straightforward than previously expected.Comment: Minor corrections (including fixing a factor of 2 in several
formulas/plots
Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT
Abstract
We use Euclidean path integrals to explore the set of bulk asymptotically AdS spacetimes with good CFT duals. We consider simple bottom-up models of bulk physics defined by Einstein-Hilbert gravity coupled to thin domain walls and restrict to solutions with spherical symmetry. The cosmological constant is allowed to change across the domain wall, modeling more complicated Einstein-scalar systems where the scalar potential has multiple minima. In particular, the cosmological constant can become positive in the interior. However, in the above context, we show that inflating bubbles are never produced by smooth Euclidean saddles to asymptotically AdS path integrals. The obstacle is a direct parallel to the well-known obstruction to creating inflating universes by tunneling from flat space. In contrast, we do find good saddles that create so-called “bag-of-gold” geometries which, in addition to their single asymptotic region, also have an additional large semi-classical region located behind both past and future event horizons. Furthermore, without fine-tuning model parameters, using multiple domain walls we find Euclidean geometries that create arbitrarily large bags-of-gold inside a black hole of fixed horizon size, and thus at fixed Bekenstein-Hawking entropy. Indeed, with our symmetries and in our class of models, such solutions provide the unique semi-classical saddle for appropriately designed (microcanonical) path integrals. This strengthens a classic tension between such spacetimes and the CFT density of states, similar to that in the black hole information problem
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