Lifshitz Gravity for Lifshitz Holography

Charles M. Melby-Thompson; Petr Horava; Tom Griffin

REVIEW

Lifshitz Gravity for Lifshitz Holography

Tom Griffin, Petr Horava, Charles M. Melby-Thompson

High Energy Physics - Theory · Submitted 20 Nov 2012 · 25 references

Pith's verdict: Clean, checkable core observation plus a genuinely new anomaly claim whose derivation lives in a companion paper that isn't out yet.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID1211.4872 (version 1)

Pith IDMSAGRKBY, Pith's permanent record of this paper and its review

CitationCharles M. Melby-Thompson, Petr Horava, Tom Griffin. "Lifshitz Gravity for Lifshitz Holography." arXiv:1211.4872 (2012). https://pith.science/paper/MSAGRKBY

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Quick read on 1211.4872. Two things matter here. First, the observation that Lifshitz spacetime is a vacuum solution of nonprojectable HL gravity with Λ = −(D+z−1)(D+z)/2 and α² = 2β(z−1)/z is short, correct as far as I can check, and conceptually the right framing: you don't need to bolt on a massive vector to get Lifshitz, you just need to change the gravity. That reframing alone is worth the paper. Second, the anomaly result: minimal HL gravity reproduces both z=2 central charges, cK = 1/(2κ²) and cV = β/(48κ²), where the Einstein-plus-vector model of [5] gives only cK. That is a real extension of their published [8], not a restatement of it, and the free-scalar counterexample with cV = −e²/(8π) is a nice touch — it settles the question of whether cV ≠ 0 theories exist at all, which someone would otherwise have asked. The unitarity bound (15) is algebraically right and the λ_U = 1/D special case at D = z is a pleasing structural byproduct. The paper is well put together and knows what it's claiming. Now the soft spot, which the authors flag themselves: the modified Hamilton-Jacobi recursion relations are asserted, not shown, with 'all technical details will appear in [23].' Letters do this routinely, so I don't hold it against them the way a referee on a full paper would — but [23] is listed as to appear, so at the moment the load-bearing step is unverifiable from anything in print. One specific thing I'd want answered when [23] lands: at z=2, Eq. 9 gives α² = β, so β/(48κ²) and α²/(48κ²) are numerically identical there. The second anomaly structure contains exactly the ∇N∇N/N² term the α² coupling controls, so the general-z coefficient would tell us whether cV really tracks β or is secretly tracking α. The paper doesn't address this and should. Minor, but worth a line. Who should read it: anyone working on Lifshitz holography, HL gravity, or anisotropic anomalies — this is the natural reference for 'HL gravity as the minimal bulk dual.' It deserves a serious referee; the vacuum-solution part stands on its own and the anomaly claim is plausible and consistent with [8], with the verification deferred to a companion that needs to appear.

Referee report

Major objections (4)

[p. 5, 'We find modified recursion relations...'] The central anomaly result cV = β/(48κ²) is the paper's headline claim, but the modified Hamilton-Jacobi recursion relations that produce it are not displayed; the text states only that they were found and solved, with all technical details deferred to [23], listed as 'to appear'. The authors acknowledge this deferral, but the consequence is that the decisive step from the action (4) to the anomaly is not checkable from this manuscript. At minimum, the modified recursion relations (or a short appendix showing how the α² term enters them) should be included so that the result is reproducible from the letter itself.
[Eq. (9) and the anomaly formula on p. 5] At z=2, Eq. (9) gives α² = β, so the claimed cV = β/(48κ²) is numerically equal to α²/(48κ²) on the Lifshitz background. The paper does not state whether cV depends on α² in general, or whether the coefficient is genuinely β rather than α². This matters because the second anomaly structure, (R - ∇N∇N/N² + ΔN/N)², contains the ∇N∇N/N² term that the α² coupling controls. Please state whether cV = β/(48κ²) holds for arbitrary α² (with the Lifshitz background then fixing α² = β), or only on the z=2 background; if the former, a sentence on why the α² term does not contribute to cV would settle the point.
[p. 6, 'The remaining coupling λ does not appear in the anomaly'] The statement that λ does not appear in the anomaly is asserted without justification. Since λ enters the kinetic term of (4) and the constraint algebra of nonprojectable HL gravity, and since the paper itself emphasizes λ's role in the graviton dispersion relation (5) and the unitarity bound (15), the reader needs to know whether λ-independence of L~(4) is exact or a feature of the D=z=2 case. A short argument, or a statement of the order at which λ would first enter, would make the 'full structure' claim precise.
[Eqs. (8)-(9)] The claim that the Lifshitz metric (2) is a vacuum solution of (4) is one of the paper's two headline results, but the check is not shown. Since the static Lifshitz metric has K_ab = 0, the verification reduces to the potential terms and is only a few lines; displaying it would make the result reproducible and would clarify the conventions for Λ, whose z=1 limit is -D(D+1)/2. This is particularly useful because the α² term is doing real work here: the pure R-2Λ theory does not admit (2) with K_ab = 0 as a solution, so the interplay between (8) and (9) deserves an explicit line.

Minor objections (5)

[p. 5, free-scalar example] The free-scalar example (cK = 1/(32π), cV = -e²/(8π)) is presented without derivation; a sketch of the ζ-function calculation, or a reference, would help the reader assess the claim that QFTs with cV ≠ 0 exist.
[p. 5, anomaly formula] The consistency check that cK = 1/(2κ²) = 1/(16πG_N) matches the relativistic result (13) should be stated explicitly; it is a nice confirmation that the HL result reduces correctly in the appropriate limit.
[Eq. (15) and surrounding discussion] Reality of D± is necessary but not sufficient for unitarity; the standard Breitenlohner-Freedman argument also requires the dimension to lie above the unitarity bound. Please state the precise condition under which (15) is the unitarity bound.
[p. 6, z → 1 limit] The remark that the z → 1 limit corresponds to α → 0, the 'unhealthy reduction' of nonprojectable HL gravity, would benefit from a reference or a sentence on why this limit is unhealthy.
[p. 4] Typos: 'iniﬁnite' should be 'infinite'.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Hořava-Lifshitz gravity may be the natural bulk dual of Lifshitz-type field theories, and its renormalization reproduces both independent coefficients of the anisotropic Weyl anomaly.

The reading

Field theories with anisotropic scaling — time rescaled by $b^z$ while space rescales by $b$ — are common in condensed matter, and the geometry that captures their symmetries is the Lifshitz spacetime. Until now, most work made that geometry a solution by adding an ad hoc massive vector field to Einstein gravity. This paper argues that a better and more minimal option is to change the gravity instead: Lifshitz spacetime is an exact vacuum solution of Hořava-Lifshitz gravity, a theory whose own short-distance scaling is anisotropic and which needs no extra matter. The payoff is a counting argument about anomalies: for $z=2$ in 2+1 boundary dimensions the anisotropic Weyl anomaly has two independent coefficients, and the relativistic Einstein-plus-vector model produces only one of them, while minimal Hořava-Lifshitz gravity produces both, each tied to a separate low-energy coupling. If the claim holds, the natural gravitational home for nonrelativistic holography is nonrelativistic gravity.

What carries the argument

The load-bearing device is a Hamilton-Jacobi formulation of holographic renormalization adapted to asymptotically Lifshitz spacetimes. The radial evolution of the on-shell action is generated by the operator $δ_D$ of anisotropic dilatations on the boundary, and the Hamilton-Jacobi equation turns into recursion relations linking the divergent terms $L^{(m)}$ of adjacent scaling dimension. One of those relations, $δ_D L^{(2D)} = -2D L^{(2D)} + ̃{L}^{(2D)}$, identifies the logarithmic coefficient $̃{L}^{(2D)}$ as the anisotropic Weyl anomaly. Solving the modified recursion relations for Hořava-Lifshitz gravity at $D=z=2$ yields the anomaly quoted above. A second piece of machinery is the asymptotic behaviour of the extra scalar graviton mode, $φ(r) ∼ r^{D_±}$ with $D_± = ½{z - D ± √{(z+D)^2 + 4D(1-z)/(1-λ)}}$, which converts reality of the dual scaling dimensions into a unitarity bound on $λ$, namely $λ ≥ 1$ or $λ ≤ λ_U = ((D-z)^2 + 4D)/(D+z)^2$, giving $λ_U = 1/D$ when $D=z$ and opening a window $1/(D+1) ≤ λ ≤ 1/D$ that flat-space stability forbids.

Extended reading notes

Core claim

The paper establishes two things. First, the Lifshitz metric $ds^2 = -(r/ℓ)^{2z}dt^2 + (r/ℓ)^2 dx^i dx^i + (ℓ/r)^2 dr^2$ solves the equations of motion of the low-energy nonprojectable Hořava-Lifshitz action with no matter fields, provided the cosmological constant and one coupling are tuned as $Λ = -(D+z-1)(D+z)/2$ and $α^2 = 2β(z-1)/z$. The foliation required to embed the geometry is simply the slicing by constant $t$. Second, holographic renormalization of this bulk theory in the case $D=z=2$ gives a logarithmic divergence whose coefficient is the most general allowed anisotropic Weyl anomaly, $A = c_K(Ĥ{K}_{ij}Ĥ{K}^{ij} - ½Ĥ{K}^2) + c_V(Ĥ{R} - Ĥ{∇}_i Ĥ{N}Ĥ{∇}^iĤ{N}/Ĥ{N}^2 + Ĥ{Δ}Ĥ{N}/Ĥ{N})^2$, with both central charges nonzero and fixed by bulk couplings: $c_K = 1/(2κ^2)$ and $c_V = β/(48κ^2)$. The relativistic competitor, Einstein gravity plus a massive vector, was already known to give $c_V = 0$ — its anomaly satisfies detailed balance — so the new model strictly enlarges the space of anomalies reachable holographically. The authors also note that the free $z=2$ Lifshitz scalar has $c_V = 0$ unless it is coupled non-minimally, and they construct such a coupling to show that field theories with $c_V ≠ 0$ exist, so the second charge is not vacuous.

Load-bearing premise

The modified Hamilton-Jacobi recursion relations for Hořava-Lifshitz gravity, and the resulting anomaly coefficient, are stated rather than derived here, with the paper saying the technicalities are involved and that all details will appear in a companion paper, so the central $c_V = β/(48κ^2)$ result cannot be checked against this text alone.

Editorial extensions

If this is right

Lifshitz holography can be done without inventing a matter sector: the geometry itself is a vacuum solution once gravity is allowed to be nonrelativistic, removing a layer of model building from every Lifshitz dual.
The two central charges of the $z=2$ anisotropic Weyl anomaly in 2+1 dimensions map onto two bulk couplings, $c_K = 1/(2κ^2)$ and $c_V = β/(48κ^2)$, so a boundary anomaly measurement becomes a statement about the gravitational action's parameters.
The detailed-balance condition on the anomaly, previously automatic in the relativistic model, becomes a special case ($β = 0$) rather than a theorem, which widens the class of boundary theories that can have gravity duals.
Bulk unitarity imposes a bound on the coupling $λ$ that is weaker than the flat-space stability bound, so the holographic setting permits parameter ranges that would be excluded by studying gravitons around flat space.
The $z → 1$ limit corresponds to $α → 0$, the known problematic reduction of nonprojectable Hořava-Lifshitz gravity, so relativistic ($z=1$) duals are not simply a smooth limit of this construction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the anomaly coefficients really are just $1/(2κ^2)$ and $β/(48κ^2)$, then the ratio $c_V/c_K = β/24$ is a clean bulk-side prediction; a boundary computation of both charges in a single strongly coupled Lifshitz theory would test the duality at the level of a number rather than a structure.
The paper's own free-field construction suggests a two-way check: the non-minimally coupled Lifshitz scalar gives $c_K = 1/(32π)$ and $c_V = -e^2/(8π)$, so the sign and size of $β$ in a putative bulk dual of that theory are, in principle, pinned down.
Because $λ$ drops out of the anomaly but controls the scalar graviton's scaling dimension, it is the natural knob for probing whether the dual field theory contains an extra light scalar operator; the unitarity window $1/(D+1) ≤ λ ≤ 1/D$ would then be a prediction about that operator's dimension rather than a technicality.
The construction says nothing about the high-energy completion of Hořava-Lifshitz gravity, so the duality is asserted only at large $N$ and small curvature; whether the $z>1$ short-distance scaling can supply its own ultraviolet completion is left as the open question that would decide how far the correspondence extends.

Original abstract

We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,055 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.35 · randomized assignment 0.01 · states quantitative result 0.46 · compares with prior results 0.90 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

background contribution method result interpretation main claim

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 argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z.	contribution 0.55	0.45	0.84	asserted 0.49
s1	First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter.	result 0.89	0.92	0.10	asserted 1.00
s2	Then we perform holographic renormalization of HL gravity, and show how it reproduces the full structure of the z=2 anisotropic Weyl anomaly in dual field theories in 2+1 dimensions, while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.	result 0.89	0.94	0.36	asserted 1.00

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

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (25)

[5]

M. Taylor, Non-relativistic Holography, arXiv:0812.0530

View on Pith Pith review arXiv
[8]

T. Griﬃn, P. Hoˇ rava, and C. M. Melby-Thompson, Conformal Lifshitz Gravity from Holography, JHEP 1205 (2012) 010, [ arXiv:1112.5660]

View on Pith Pith review arXiv 2012
[23]

T. Griﬃn, P. Hoˇ rava, and C. M. Melby-Thompson, Anisotropic Weyl Anomalies and Lifshitz Holography (to appear)

View on Pith
[1]

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics . Cambridge U.P., 1995

View on Pith 1995
[2]

P. Hoˇ rava,Membranes at Quantum Criticality , JHEP 03 (2009) 020, [ arXiv:0812.4287]

View on Pith Pith review arXiv 2009
[3]

P. Hoˇ rava,Quantum Gravity at a Lifshitz Point , Phys. Rev. D79 (2009) 084008, [arXiv: 0901.3775 ]

View on Pith Pith review arXiv 2009
[4]

S. Kachru, X. Liu, and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points , Phys.Rev. D78 (2008) 106005, [ arXiv:0808.1725]

View on Pith Pith review arXiv 2008
[6]

D. Blas, O. Pujol` as, and S. Sibiryakov, Consistent Extension of Hoˇ rava Gravity, Phys.Rev.Lett. 104 (2010) 181302, [ arXiv:0909.3525]

View on Pith Pith review arXiv 2010
[7]

P. Hoˇ rava,General Covariance in Gravity at a Lifshitz Point , Class. Quant. Grav. 28 (2011) 114012, [ arXiv:1101.1081]

View on Pith Pith review arXiv 2011
[9]

M. Baggio, J. de Boer, and K. Holsheimer, Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model , arXiv:1112.6416

View on Pith Pith review arXiv
[10]

M. Henningson and K. Skenderis, The Holographic Weyl Anomaly , JHEP 9807 (1998) 023, [arXiv:hep-th/9806087]. – 7 –

View on Pith Pith review arXiv 1998
[11]

P. Kraus, F. Larsen, and R. Siebelink, The Gravitational Action in Asymptotically AdS and Flat Spacetimes, Nucl. Phys. B563 (1999) 259–278, [ arXiv:hep-th/9906127]

View on Pith Pith review arXiv 1999
[12]

J. de Boer, E. P. Verlinde, and H. L. Verlinde, On the Holographic Renormalization Group , JHEP 0008 (2000) 003, [ arXiv:hep-th/9912012]

View on Pith Pith review arXiv 2000
[13]

K. Skenderis, Lecture Notes on Holographic Renormalization , Class. Quant. Grav. 19 (2002) 5849, [ arXiv:hep-th/0209067]

View on Pith Pith review arXiv 2002
[14]

J. de Boer, The Holographic Renormalization Group , Fortsch.Phys. 49 (2001) 339–358, [arXiv:hep-th/0101026]

View on Pith Pith review arXiv 2001
[15]

M. Fukuma, S. Matsuura, and T. Sakai, Holographic Renormalization Group , Prog. Theor. Phys. 109 (2003) 489, [ arXiv:hep-th/0212314]

View on Pith Pith review arXiv 2003
[16]

S. F. Ross and O. Saremi, Holographic Stress Tensor for Non-relativistic Theories , JHEP 0909 (2009) 009, [ arXiv:0907.1846]

View on Pith Pith review arXiv 2009
[17]

S. F. Ross, Holography for Asymptotically Locally Lifshitz Spacetime s, Class. Quant. Grav. 28 (2011) 215019, [ arXiv:1107.4451]

View on Pith Pith review arXiv 2011
[18]

R. Mann and R. McNees, Holographic Renormalization for Asymptotically Lifshitz Spacetimes, JHEP 1110 (2011) 129, [ arXiv:1107.5792]

View on Pith Pith review arXiv 2011
[19]

M. Baggio, J. de Boer, and K. Holsheimer, Hamilton-Jacobi Renormalization for Lifshitz Spacetime, arXiv:1107.5562

View on Pith Pith review arXiv
[20]

P. Hoˇ rava and C. M. Melby-Thompson, Anisotropic Conformal Inﬁnity , Gen. Rel. Grav. 43 (2010) 1391, [ arXiv:0909.3841]

View on Pith Pith review arXiv 2010
[21]

I. Papadimitriou and K. Skenderis, AdS/CFT Correspondence and Geometry , arXiv:hep-th/0404176

View on Pith Pith review arXiv
[22]

I. Papadimitriou and K. Skenderis, Correlation Functions in Holographic RG Flows , JHEP 0410 (2004) 075, [ arXiv:hep-th/0407071]

View on Pith Pith review arXiv 2004
[24]

S. Janiszewski and A. Karch, String Theory Embeddings of Non-relativistic Field Theori es and their Holographic Hoˇ rava Gravity Duals, arXiv:1211.0010

View on Pith Pith review arXiv
[25]

S. Janiszewski and A. Karch, Non-relativistic Holography from Hoˇ rava Gravity, arXiv:1211.0005. – 8 –

View on Pith Pith review arXiv

Forward citations

Cited by 14 Pith papers

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

Renormalization of Horava Gravity
hep-th 2015-12 conditional novelty 7.0 of 10

Projectable Horava gravity is shown to be perturbatively renormalizable, using a two-parameter family of gauges that renders all propagators regular and a background-covariant formalism that preserves gauge invariance...
Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry
hep-th 2015-04 accept novelty 7.0 of 10

Dynamical torsional Newton-Cartan geometry is shown to be equivalent to Horava-Lifshitz gravity, with an explicit dictionary and matching effective action.
Scalar Field Theories with Polynomial Shift Symmetries
hep-th 2014-12 conditional novelty 7.0 of 10

The unique lowest-derivative N-point Lagrangian invariant under a linear polynomial shift is the equal-weight sum over all labeled trees with N vertices, and superposing such tree sums with exact invariants generates ...
Fractons, dipole symmetries and curved spacetime
hep-th 2021-11 conditional novelty 6.0 of 10

Complex scalar theories with dipole symmetry couple to arbitrary Aristotelian (boost-free) spacetimes, and the dynamical symmetric-tensor gauge theory couples only to geometries obeying a specific curvature constraint.
Ho\v{r}ava gravity is asymptotically free (in 2+1 dimensions)
hep-th 2017-06 conditional novelty 6.0 of 10

Projectable Hořava gravity in 2+1 dimensions has a one-loop ultraviolet fixed point at λ = 15/14 with vanishing coupling, making the theory asymptotically free in that truncation.

Show 9 more citing papers

Symmetries and Couplings of Non-Relativistic Electrodynamics
hep-th 2016-07 accept novelty 6.0 of 10

Galilean electrodynamics has an off-shell Lifshitz scale symmetry for any critical exponent z, and the electric and magnetic limits carry an infinite-dimensional Galilean conformal plus U(1) current algebra in any dimension.
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.
Torsional Newton-Cartan Geometry and the Schr\"odinger Algebra
hep-th 2014-09 conditional novelty 6.0 of 10

Gauging the Schrödinger algebra with suitable curvature constraints produces twistless torsional Newton-Cartan geometry, and adding a Stückelberg scalar plus an extra conformal symmetry reproduces the boundary geometr...
Lifshitz holography: The whole shebang
hep-th 2014-08 conditional novelty 6.0 of 10

A recursive algorithm built on two commuting functional operators generates the full holographic dictionary, including counterterms, Fefferman-Graham expansions, Ward identities and anomalies, for asymptotically local...
Lifshitz Space-Times for Schroedinger Holography
hep-th 2014-09 conditional novelty 5.0 of 10

Asymptotically locally Lifshitz space-times are shown to be holographically dual to field theories whose sources transform under the Schrödinger algebra and form torsional Newton-Cartan geometry.
Review on Non-Relativistic Gravity
gr-qc 2022-12 accept novelty 3.0 of 10

Expanding general relativity in powers of 1/c yields a 'type II' Newton-Cartan geometry whose action reproduces Newton's Poisson equation off shell and whose torsionful solutions describe strong gravitational fields.
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...
Ho\v{r}ava Gravity at a Lifshitz Point: A Progress Report
gr-qc 2017-01 conditional novelty 1.0 of 10

Horava gravity remains an unfinished but actively studied route to quantum gravity, with four main versions whose viability depends on narrow parameter choices and unresolved strong-coupling and cosmological tests.

How later papers used it

72 later papers cite it

Evidence: substantial. 70 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 112 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper

Used the ADM metric to describe the four dimensional spacetime, noting that the breaking of symmetry between time and space in Hořava-Lifshitz gravity makes this convenient.

Analysis of s-wave, p-wave and d-wave holographic superconductors in Ho\v{r}ava-Lifshitz gravity (2018) · 0.83 · paraphrased: the licence does not allow quoting

How the literature uses it

70 arXiv papers cite this in 110 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 · 65 sentences without a confident label

Builds on it 1 paper

The freedom to add such a term to the action and thereby change the corresponding anomaly coefficient was previously pointed out in [ref] for a purely spatial anomaly of a free Lifshitz scalar in $d=z=2$, but it is in fact more general.

Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization · Ambiguity of the Anomaly Coefficients? · 0.81

Uses its method or tool 1 paper

Due to the breaking of the symmetry between time and space in Hořava-Lifshitz gravity, it is convenient to describe the four dimensional spacetime in terms of the ADM metric [ref] 18 ds^2=-N^2dt^2+γ_ij(dx^i+N^idt)(dx^j+N^jdt), where $i,j=1,2,3$, or equivalently, one has 19 g_μν = ( [ g_00 g_0j; g_i0 g_ij; ] )=( [ -N^2+N_kN^k N_j; N_i γ_ij; ] ), g^μν= ( [ g^00 g^0j; g^i0 g^ij; ] )=( [ -1/N^2 N^j/N^2; N^i/N^2 γ^ij-N^iN^j/N^2; ] ).

Analysis of s-wave, p-wave and d-wave holographic superconductors in Ho\v{r}ava-Lifshitz gravity · An unified equations of motion for holographic superconductors · 0.83

Compares with it 3 papers

This coefficient was previously computed (with no restrictions on the lapse function) in [ref] for $Ω_(m)=0$ and in [ref] for $Ω_(2)=Ω_(1)=0$, $Ω_(0)0$.

Heat kernel methods for Lifshitz theories · Case $z=d=2$ · 0.96
This is consistent with previous results (see [ref] ), that considered only the case where the Frobenius condition is satisfied (and therefore only the anomaly $A_4^( 0,4,0 ) = ( R̂ + ∇̅_αa^α )^2$).

Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization · Results for the Three Point Function and the Anomaly · 0.87
In summary, the general solution of the topological black holes in HL$_d+1$ gravity is given in Eq.([ref]) with Ñ^2(r) i = i C_N^2 r^2λ^±_N, f(r) i = i k - 2Λ_W/(d-1)(d-2) r^2 - C_F r^λ_F^±. it is worthy of notice the difference between the metric of Lifshitz gravity in Refs. [ref] and the metric of topological neutral black holes in HL gravity with $k=0$ case.

Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity · $z=d$ HL$_d+1$ gravity · 0.99

Cites it as support 3 papers

Indeed, recently it was showed that the Lifshitz spacetime ([ref]) is a vacuum solution of Hořava gravity in (2+1) dimensions, and that the full structure of the $z=2$ anisotropic Weyl anomaly can be reproduced in dual field theories [ref] , while its minimal relativistic gravity counterpart yields only one of two independent central charges in the anomaly.

Ho\v{r}ava Gravity at a Lifshitz Point: A Progress Report · Non-relativistic Gauge/Gravity Duality · 0.97
This stems from the fact that these anomalies are of second order in derivatives in the flat spacetimes [ref] , hence they are harmless and allow to avoid the vanishing of conformal anomaly criteria [ref] .

Finite Action Principle and Horava-Lifshitz Gravity: early universe, black holes and wormholes · Conclusions and discussion · 0.96
Given that these spacetimes are vacuum solutions of Hořava gravity lends evidence to the proposal that this alternate theory of gravity is dual to generic NR QFTs [ref] .

Asymptotically hyperbolic black holes in Horava gravity · Discussion · 0.97

Cites it as background 34 papers

The body of literature most relevant to us here, however, concerns earlier work on holographic renormalization and the holographic dictionary for asymptotically Lifshitz spacetimes [ref] .

Lifshitz holography: The whole shebang · Introduction · 0.94
A number of bottom-up models have been suggested in the literature giving rise to this Lifshitz solution, such as Einstein-Proca, Einstein-Maxwell-Dilaton and Einstein-$p$-form actions [ref] (see [ref] for a general analysis of holography for bottom-up Lifshitz models, including also the hyperscaling violating solutions obtained in [ref] ), or using the nonrelativistic gravity theory of Hořava-Lifshitz [ref] .

Holographic quenches towards a Lifshitz point · Introduction · 0.93
Various quantum aspects of Lifshitz theories, in particular in the context of HG, have been considered in [ref] .

Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity · Explicit calculations and renormalization group flow · 1.00

What it cites · 33 sentences without a confident label

Uses the method or tool of 4 papers

They can be classified by solving a cohomological problem [ref] designed to automatically incorporate the Wess-Zumino consistency conditions on the anomaly.

Conformal Lifshitz Gravity from Holography · Introduction · 0.93
To calculate these divergent terms, we use the Hamiltonian form of holographic renormalization, as developed for relativistic AdS/CFT in [ref] and extended to the asymptotically Lifshitz case in [ref] following [ref] .

Holography for asymptotically locally Lifshitz spacetimes · Introduction · 0.89
To calculate these divergent terms, we use the Hamiltonian form of holographic renormalization, as developed for relativistic AdS/CFT in [ref] and extended to the asymptotically Lifshitz case in [ref] following [ref] .

AdS/CFT correspondence and Geometry · Introduction · 0.89

Cites as support 4 papers

Further evidence for the universality of this minimal model of Lifshitz holography comes from the analysis of anisotropic Weyl anomalies in holographic renormalization, initiated in [ref] (and also later in [ref] ).

Conformal Lifshitz Gravity from Holography · Introduction · 1.00
Further evidence for the universality of this minimal model of Lifshitz holography comes from the analysis of anisotropic Weyl anomalies in holographic renormalization, initiated in [ref] (and also later in [ref] ).

Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model · Introduction · 1.00
Our results, and those of [ref] , thus provide further evidence for the picture proposed originally in [ref] , that the natural arena for nonrelativistic holography is nonrelativistic HL gravity.

Non-relativistic holography from Horava gravity · Introduction · 0.98

Cites as background 6 papers

More recently, in a seemingly unrelated development, anisotropic Lifshitz-type scaling ([ref]) has played a central role in the new approach to quantum gravity initiated in [ref] and commonly referred to as Hořava-Lifshitz (HL) gravity.

Membranes at Quantum Criticality · Introduction · 0.89
More recently, in a seemingly unrelated development, anisotropic Lifshitz-type scaling ([ref]) has played a central role in the new approach to quantum gravity initiated in [ref] and commonly referred to as Hořava-Lifshitz (HL) gravity.

Quantum Gravity at a Lifshitz Point · Introduction · 0.89
It is useful to think of this theory as residing at the spacetime boundary $r→∞$ of the $D+2$ dimensional asymptotically Lifshitz spacetime, with $ĝ_ij$, $N̂_i$ and $N̂$ being the components of the appropriately defined (anisotropic conformal class of the) boundary metric [ref] .

Conformal Lifshitz Gravity from Holography · Introduction · 0.80

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [5]

M. Taylor, Non-relativistic Holography, arXiv:0812.0530

View on Pith Pith review arXiv

[2] [8]

T. Griﬃn, P. Hoˇ rava, and C. M. Melby-Thompson, Conformal Lifshitz Gravity from Holography, JHEP 1205 (2012) 010, [ arXiv:1112.5660]

View on Pith Pith review arXiv 2012

[3] [23]

T. Griﬃn, P. Hoˇ rava, and C. M. Melby-Thompson, Anisotropic Weyl Anomalies and Lifshitz Holography (to appear)

View on Pith

[4] [1]

P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics . Cambridge U.P., 1995

View on Pith 1995

[5] [2]

P. Hoˇ rava,Membranes at Quantum Criticality , JHEP 03 (2009) 020, [ arXiv:0812.4287]

View on Pith Pith review arXiv 2009

[6] [3]

P. Hoˇ rava,Quantum Gravity at a Lifshitz Point , Phys. Rev. D79 (2009) 084008, [arXiv: 0901.3775 ]

View on Pith Pith review arXiv 2009

[7] [4]

S. Kachru, X. Liu, and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points , Phys.Rev. D78 (2008) 106005, [ arXiv:0808.1725]

View on Pith Pith review arXiv 2008

[8] [6]

D. Blas, O. Pujol` as, and S. Sibiryakov, Consistent Extension of Hoˇ rava Gravity, Phys.Rev.Lett. 104 (2010) 181302, [ arXiv:0909.3525]

View on Pith Pith review arXiv 2010

[9] [7]

P. Hoˇ rava,General Covariance in Gravity at a Lifshitz Point , Class. Quant. Grav. 28 (2011) 114012, [ arXiv:1101.1081]

View on Pith Pith review arXiv 2011

[10] [9]

M. Baggio, J. de Boer, and K. Holsheimer, Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model , arXiv:1112.6416

View on Pith Pith review arXiv

[11] [10]

M. Henningson and K. Skenderis, The Holographic Weyl Anomaly , JHEP 9807 (1998) 023, [arXiv:hep-th/9806087]. – 7 –

View on Pith Pith review arXiv 1998

[12] [11]

P. Kraus, F. Larsen, and R. Siebelink, The Gravitational Action in Asymptotically AdS and Flat Spacetimes, Nucl. Phys. B563 (1999) 259–278, [ arXiv:hep-th/9906127]

View on Pith Pith review arXiv 1999

[13] [12]

J. de Boer, E. P. Verlinde, and H. L. Verlinde, On the Holographic Renormalization Group , JHEP 0008 (2000) 003, [ arXiv:hep-th/9912012]

View on Pith Pith review arXiv 2000

[14] [13]

K. Skenderis, Lecture Notes on Holographic Renormalization , Class. Quant. Grav. 19 (2002) 5849, [ arXiv:hep-th/0209067]

View on Pith Pith review arXiv 2002

[15] [14]

J. de Boer, The Holographic Renormalization Group , Fortsch.Phys. 49 (2001) 339–358, [arXiv:hep-th/0101026]

View on Pith Pith review arXiv 2001

[16] [15]

M. Fukuma, S. Matsuura, and T. Sakai, Holographic Renormalization Group , Prog. Theor. Phys. 109 (2003) 489, [ arXiv:hep-th/0212314]

View on Pith Pith review arXiv 2003

[17] [16]

S. F. Ross and O. Saremi, Holographic Stress Tensor for Non-relativistic Theories , JHEP 0909 (2009) 009, [ arXiv:0907.1846]

View on Pith Pith review arXiv 2009

[18] [17]

S. F. Ross, Holography for Asymptotically Locally Lifshitz Spacetime s, Class. Quant. Grav. 28 (2011) 215019, [ arXiv:1107.4451]

View on Pith Pith review arXiv 2011

[19] [18]

R. Mann and R. McNees, Holographic Renormalization for Asymptotically Lifshitz Spacetimes, JHEP 1110 (2011) 129, [ arXiv:1107.5792]

View on Pith Pith review arXiv 2011

[20] [19]

M. Baggio, J. de Boer, and K. Holsheimer, Hamilton-Jacobi Renormalization for Lifshitz Spacetime, arXiv:1107.5562

View on Pith Pith review arXiv

[21] [20]

P. Hoˇ rava and C. M. Melby-Thompson, Anisotropic Conformal Inﬁnity , Gen. Rel. Grav. 43 (2010) 1391, [ arXiv:0909.3841]

View on Pith Pith review arXiv 2010

[22] [21]

I. Papadimitriou and K. Skenderis, AdS/CFT Correspondence and Geometry , arXiv:hep-th/0404176

View on Pith Pith review arXiv

[23] [22]

I. Papadimitriou and K. Skenderis, Correlation Functions in Holographic RG Flows , JHEP 0410 (2004) 075, [ arXiv:hep-th/0407071]

View on Pith Pith review arXiv 2004

[24] [24]

S. Janiszewski and A. Karch, String Theory Embeddings of Non-relativistic Field Theori es and their Holographic Hoˇ rava Gravity Duals, arXiv:1211.0010

View on Pith Pith review arXiv

[25] [25]

S. Janiszewski and A. Karch, Non-relativistic Holography from Hoˇ rava Gravity, arXiv:1211.0005. – 8 –

View on Pith Pith review arXiv