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

Cynthia Keeler; Gino Knodel; James T. Liu

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

Cynthia Keeler, Gino Knodel, James T. Liu

High Energy Physics - Theory · Submitted 26 Aug 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.43 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.14 · mentions code or data availability 0.01.

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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 we expect 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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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.81	0.88	0.05	asserted 0.80
s1	For a large class of such spacetimes, there exist null geodesics which do not reach the boundary.	result 0.96	0.62	0.05	asserted 0.95
s2	Therefore classically we expect some information is trapped in the bulk and thus invisible at the boundary.	interpretation 0.91	0.20	0.08	hedged possibility 0.88
s3	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.	result 0.99	0.93	0.32	asserted 1.00
s4	We use these modes to show that no smearing function exists for pure Lifshitz spacetime, nor for any flow which includes a Lifshitz region.	result 0.99	0.94	0.36	asserted 1.00
s5	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.	result 0.98	0.93	0.68	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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Original 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 we expect 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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References

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
hep-th 2013-11 accept novelty 7.0 of 10

The boundary geometry of z=2 Lifshitz holography is torsional Newton-Cartan geometry, and the paper derives the boundary stress-energy tensor, Ward identities, and anisotropic Weyl anomaly on it.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
hep-th 2016-04 conditional novelty 6.0 of 10

Three-dimensional Horava-Lifshitz gravity is shown to equal a Chern-Simons gauge theory on extended Bargmann, Newton-Hooke, and Schroedinger algebras, with the Schroedinger case yielding a new z=2 Lifshitz-vacuum gravity.
Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
hep-th 2015-02 conditional novelty 6.0 of 10

Lifshitz holography is dual to field theories on torsional Newton-Cartan backgrounds, where a background vector field can promote a global U(1) to a local symmetry and realize Schrödinger symmetry.
Lifshitz holography
hep-th 2015-12 conditional novelty 3.0 of 10

A structured review of the holographic dictionary for Lifshitz backgrounds, arguing that the bulk matter supporting the geometry sources the non-relativistic energy-momentum complex plus scalar operators rather than a...

How the literature uses it

16 arXiv papers cite this in 33 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 20 sentences without a confident label

Builds on it 1 paper

This classical intuition was confirmed in [ref] for the case of bulk scalars, and, as we have shown above, generalizes to bulk fermions as well.

Holographic Lifshitz fermions and exponentially suppressed spectral weight · Discussion · 0.85

Uses its method or tool 2 papers

After switching to the $ρ̂$ coordinates defined in ([ref]), the spectral function can be approximated by [The additional prefactor of $|k⃗|^2νz$ arises from letting $ϵ→|k⃗|^-zϵ$, which is the proper UV cutoff needed to cancel the log-divergence of the integral. ] [ref] [equation] Here $K$ is a normalization constant and [equation] The additional $1/ρ̂^2$ term is equivalent to an effective shift $ν^2→ν^2+1/4$, which is necessary for consistency of the WKB approximation for $1/x^2$ potentials [ref] .

Universal features of Lifshitz Green's functions from holography · WKB analysis of the spectral function · 0.91
The behavior alluded to above can be quantified using a WKB approximation [ref] .

Spatial Anisotropy in Nonrelativistic Holography · WKB Approximation · 0.97

Cites it as support 1 paper

The exponential suppression of spectral weight below the non-relativistic dispersion relation is a universal feature of Lifshitz spacetimes, and furthermore provides an obstruction to the construction of a smearing function for the bulk reconstruction of local boundary operators [ref] .

Seeing bulk perturbations in Lifshitz holography · Conclusions · 1.00

Cites it as background 7 papers

Finding which CFT quantities encode the bulk and, if so, in what ways have been actively pursued recently, e.g. [ref] .

Scanning Tunneling Macroscopy, Black Holes, and AdS/CFT Bulk Locality · Introduction · 1.00
It is well-known that only radial null geodesics are able to reach the boundary of Lifshitz spacetime [ref] , leading to various subtleties in the treatment of holographic quantities and must be dealt with care [ref] .

Kasner-type singularities and solitons with Lifshitz asymptotics · Introduction · 0.95
Nevertheless, there are some challenges associated with studying holographic duality in nonrelativistic backgrounds, see e.g., [ref] .

Entanglement Wedge Cross Section Growth During Thermalization · Introduction · 0.95

What it cites · 33 sentences without a confident label

Compares with 3 papers

Let us now check that the result obtained for the toy-model [ref] is indeed correct also for the exact numerical solution found in [ref] (here $d=2$).

Higher derivative corrections to Lifshitz backgrounds · No smearing function $⇔$ singularities? · 0.88
In particular, we cannot have a situation akin to Figure 5 in [ref] , where the potential has a dip allowing trapped modes to become oscillating again close to the boundary. ].

AdS black holes, the bulk-boundary dictionary, and smearing functions · Adding trapped modes via deformations · 0.81
in agreement with [ref] when continued to Euclidean space.

Gravity Duals of Lifshitz-like Fixed Points · A Specific Example: $z=2$ Lifshitz · 0.98

Cites as support 1 paper

It is, however, felt by strings that fall towards the horizon [ref] .]

Lifshitz Singularities · No smearing function $⇔$ singularities? · 0.97

Cites as background 29 papers

Much recent progress has been made in creating a complete bulk/boundary dictionary for nonrelativistic systems [ref] .

Holographic Renormalization for Asymptotically Lifshitz Spacetimes · Introduction · 0.91
Much recent progress has been made in creating a complete bulk/boundary dictionary for nonrelativistic systems [ref] .

Holographic stress tensor for non-relativistic theories · Introduction · 0.91
Much recent progress has been made in creating a complete bulk/boundary dictionary for nonrelativistic systems [ref] .

Holography for asymptotically locally Lifshitz spacetimes · Introduction · 0.91

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