Implications of bulk causality for holography in AdS

Kleban, Matthew; McGreevy, John; Thomas, S.

doi:10.1088/1126-6708/2004/03/006

Cited by 17 publications

(27 citation statements)

References 12 publications

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“…1; only these values of z are suitable for a holographic construction. Notice that there could be causality issues of the type we have described when the space is asymptotically AdS (z ¼ 1) if there is matter in the bulk that violates the NEC [29,30].…”

Section: Speed Of Light and The Null Energy Conditionmentioning

confidence: 92%

Null energy condition and causality in Lifshitz holography

Hoyos

Koroteev

2010

Phys. Rev. D

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We use a WKB approximation to establish a relation between the wave front velocity in a strongly coupled theory and the local speed of light in a holographic dual, with our main focus put on systems with Lifshitz scaling with dynamical exponent z. We then use Einstein equations to relate the behavior of the local speed of light in the bulk with the null energy condition (NEC) for bulk matter, and we show that it is violated for Lifshitz backgrounds with z < 1. We study signal propagation in the gravity dual and show that violations of the NEC are incompatible with causality in the strongly coupled theory, ruling out as holographic models Lifshitz backgrounds with z < 1. We argue that causality violations in z < 1 theories will show up in correlators as superluminal modes and confirm this for a particular example with z ¼ 1=2. Finally, as an application, we use z < 1 solutions to uncover regions of the parameter space of curvature squared corrections to gravity where the NEC can be violated.

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Section: Speed Of Light and The Null Energy Conditionmentioning

confidence: 92%

Null energy condition and causality in Lifshitz holography

Hoyos

Koroteev

2010

Phys. Rev. D

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“…Our arguments closely follow those of [38,39], where first steps towards generalizing smearing functions to spaces other than pure AdS were made. It is important to note that the failure to construct a smearing function, which would connect local bulk data to local boundary data, does not necessarily prevent reconstruction of the bulk metric from nonlocal boundary data, such as JHEP01(2014)062 the 2-point boundary correlators considered in [40][41][42][43][44][45][46]. In this paper we will nonetheless concentrate on the failure of the local-to-local map embodied by the smearing function.…”

Section: Jhep01(2014)062mentioning

confidence: 99%

“…One possibility that comes to mind is to make use of non-local operators in the field theory, such as Wilsonloops [59]. Even more simply, as in [40,42,46], we could consider boundary-boundary 2-point functions, which are also in some sense non-local boundary objects. At the very least, our analysis demonstrates that some parts of the holographic dictionary for nonrelativistic gauge/gravity dualities are more intricate than in the well-understood AdS/CFT case.…”

Section: Jhep01(2014)062mentioning

confidence: 99%

What do non-relativistic CFTs tell us about Lifshitz spacetimes?

Keeler

Knodel

Liu

2014

J. High Energ. Phys.

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Abstract:We study the reconstructability of (d + 2)-dimensional bulk spacetime from (d+1)-dimensional boundary data, particularly concentrating on backgrounds which break (d+1)-dimensional Lorentz invariance. For a large class of such spacetimes, there exist null geodesics which do not reach the boundary. Therefore classically one might guess some information is trapped in the bulk and thus invisible at the boundary. We show that this classical intuition correctly predicts the quantum situation: whenever there are null geodesics which do not reach the boundary, there are also "trapped scalar modes" whose boundary imprint is exponentially suppressed. We use these modes to show that no smearing function exists for pure Lifshitz spacetime, nor for any flow which includes a Lifshitz region. Indeed, for any (planar) spacetime which breaks (d + 1)-dimensional Lorentz invariance at any radius, we show that local boundary data cannot reconstruct complete local bulk data.

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“…In order to provide a proof by explicit construction, we start with AdS d+1 in Poincaré coordinates: 10) where is the AdS scale. By exploiting the translational symmetries of these coordinates, it is easy to show that any null geodesic anchored at a fixed boundary point (t = τ, x i = 0) can be parametrized in terms of some affine parameterλ as…”

Section: A2 Explicit Constructionmentioning

confidence: 99%

The gravity dual of boundary causality

Engelhardt

Fischetti

2016

Class. Quantum Grav.

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Abstract:In gauge/gravity duality, points which are not causally related on the boundary cannot be causally related through the bulk; this is the statement of boundary causality. By the Gao-Wald theorem, the averaged null energy condition in the bulk is sufficient to ensure this property. Here we proceed in the converse direction: we derive a necessary as well as sufficient condition for the preservation of boundary causality under perturbative (quantum or stringy) corrections to the bulk. The condition that we find is a (background-dependent) constraint on the amount by which light cones can "open" over all null bulk geodesics. We show that this constraint is weaker than the averaged null energy condition.

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Implications of bulk causality for holography in AdS

Cited by 17 publications

References 12 publications

Null energy condition and causality in Lifshitz holography

Null energy condition and causality in Lifshitz holography

What do non-relativistic CFTs tell us about Lifshitz spacetimes?

The gravity dual of boundary causality

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