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Lorentz violation, Gravity, Dissipation and Holography

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Elias Kiritsis

High Energy Physics - Theory · Submitted 10 Jul 2012 · 86 references

Pith's verdict: The holographic drag computation in hyperscaling-violating Lifshitz backgrounds is real and checkable; the abstract's 'must always be fields in a gravitational sector' is stronger than what sections 3 and 4 actually derive.

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arXiv ID1207.2325 (version 2)
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CitationElias Kiritsis. "Lorentz violation, Gravity, Dissipation and Holography." arXiv:1207.2325 (2012). https://pith.science/paper/PVJVLN7Z
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The paper

The paper claims

Lorentz violation cannot be written into a law of physics; it must come from a background field, the paper argues, and that field makes speeding particles radiate in a calculable way.

The reading

Kiritsis argues that a theory which breaks Lorentz invariance cannot simply be coupled to gravity as written: the symmetry that gravity gauges has to be restored, exactly as a Stückelberg field restores a gauged $U(1)$. The restoration turns every Lorentz-violating coupling into a tensor field living in a gravitational sector, so diffeomorphism invariance survives untouched and coordinate frames change the way Einstein said they do, with the couplings transforming as tensors along the way. The payoff is a reframing: Lorentz violation is not a modified law of motion but a background — a fifth force — generated by energy, charge, or fields we have not accounted for. The paper then treats a concrete realisation, a brane moving through a higher-dimensional gravitational background whose induced speed of light is energy-dependent, and uses the holographic trailing-string construction to compute how a heavy particle moving through such a medium loses energy. In scale-invariant backgrounds the drag and the dissipation rate come out as powers fixed by two exponents, the Lifshitz exponent $z$ and the hyperscaling-violation exponent $θ$.

What carries the argument

Two pieces carry the paper. The first is Stückelberg promotion: any coupling that breaks a local symmetry is rewritten by introducing a field that shifts under the symmetry so the combination is invariant, which here converts each Lorentz-violating constant into a tensor field of a gravitational sector. The second is the trailing string in a generalized Lifshitz metric $ds^2 ∼ (r/ℓ)^{(θ-2)/(2-z)}[-f(r)dt^2 + dr^2/f(r) + dx_idx^i]$ with $f(r) = f_0 (r/ℓ)^{2(1-z)/(2-z)}$. Forcing the string endpoint to move at constant velocity, the worldsheet develops a horizon at $r_s$ where $f(r_s) = v^2$; requiring the numerator and denominator of $ξ'(r)$ to change sign at the same point fixes the conserved momentum and hence the drag. Quadratic fluctuations about that solution give the retarded force correlators, and their low-frequency limit gives friction and diffusion, with the Einstein relation holding at the worldsheet temperature rather than the bulk one.

Extended reading notes

Core claim

The central claim is that Lorentz violation in quantum field theory is always environmental. The argument is a symmetry-restoration one: gravity makes translations and Lorentz transformations local, and explicitly breaking a local symmetry gives a sick quantum theory, so the only consistent route is to restore it. Promoting the offending couplings to fields — a vector coupling $b_μ$ becomes $g^{μν}A_μ(x)$ with $A_μ$ transforming as a vector under general coordinate transformations — leaves diffeomorphism invariance intact and reproduces the original violating theory in a Minkowski background where $A_μ = b_μ$. From this the author draws the identification Lorentz violation $≃$ fifth forces, and notes that the Hořava-Lifshitz construction is not an exception but a generally covariant theory after Stückelberg rearrangement. The second half delivers the quantitative part: in a brane setup the effective speed of light on the worldvolume is $c^2_{eff} = f(r) ≤ c^2_{UV}$, falls with energy as $c_{eff} ∼ E^{2(z-1)/(2z-θ)}$, and a string trailing a forced quark through the dual generalized Lifshitz geometry gives a drag $F_{drag} = -v/(2πℓ_s^2) (v/√f_0)^{(2-θ)/(z-1)}$, an energy-loss rate $dE/dt ∼ E^{(2z-θ)/(θ-2)}$, and Langevin diffusion constants obeying $κ_{⊥,||} = 2T_s χ_{⊥,||}$ with an emergent worldsheet temperature $T_s$.

Load-bearing premise

The argument assumes the ultraviolet fixed point of the theory is Lorentz invariant, so that all violation is an infrared, environmental effect; the author concedes in section 4.1 that a Lifshitz ultraviolet fixed point would change the conclusion and make generalized Hořava-Lifshitz gravity the natural gravitational partner.

Editorial extensions

If this is right

  • Every Lorentz-violation search becomes a search for a new force: an anomaly in particle propagation should be attributable to a background tensor field sourced by energy, charge, or an unknown sector, not to a modified dispersion law.
  • Coordinate transformations remain the standard ones, so the question of 'which frame' for a Lorentz-violating experiment has a definite answer once the background fields are transformed too.
  • In a strongly coupled medium with a gravity dual, the energy loss of a fast probe is fixed by two numbers, $z$ and $θ$, ranging from very slow to exponential, so a measured dissipation rate would read off the critical exponents of the medium.
  • The same construction supplies a holographic formula for how the effective speed of light runs with energy, $c_{eff} ∼ E^{2(z-1)/(2z-θ)}$, which is the RG-flow statement the paper offers in place of 'is Lorentz invariance an accident of low energies'.
  • Because the worldsheet horizon exists even without a regular bulk horizon, the fluctuation calculation suggests a Hawking-like fluctuation spectrum in Lifshitz backgrounds where no such effect was previously known.

Reading between the lines

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

  • If the promotion argument is right, the sharp experimental signature of fundamental Lorentz violation is not an energy-dependent dispersion relation but a species-dependent one: different brane stacks sit at different radial positions and inherit different $c_{eff}$, which is a statement about where fields live rather than about how they move.
  • The dissipation formula $dE/dt ∼ E^{(2z-θ)/(θ-2)}$ is a rare case where a strongly coupled transport coefficient is written purely in terms of static critical exponents, which suggests using measured cosmic-ray or neutrino energy loss as a probe of $z$ and $θ$ rather than of the Lorentz-violating coupling itself.
  • The author's own remark that the trailing-string calculation becomes unreliable at high velocity, and that the effective transverse mass turns negative there, points to a real open problem: whether the apparent instability is a property of the background or an artefact of the probe approximation, which a full fluctuation analysis with backreaction would settle.
  • Since the argument reduces all Lorentz violation to background expectation values, a clean test would be to look for a Lorentz-violating QFT vacuum with no external source at all; finding one would put the 'all Lorentz violation is environmental' identification under direct strain.
Original abstract

We reconsider Lorentz Violation (LV) at the fundamental level. We show that Lorentz Violation is intimately connected with gravity and that LV couplings in QFT must always be fields in a gravitational sector. Diffeomorphism invariance must be intact and the LV couplings transform as tensors under coordinate/frame changes. Therefore searching for LV is one of the most sensitive ways of looking for new physics, either new interactions or modifications of known ones. Energy dissipation/Cerenkov radiation is shown to be a generic feature of LV in QFT. A general computation is done in strongly coupled theories with gravity duals. It is shown that in scale invariant regimes, the energy dissipation rate depends non-triviallly on two characteristic exponents, the Lifshitz exponent and the hyperscaling violation exponent.

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, 5,465 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We reconsider Lorentz Violation (LV) at the fundamental level. We show that Lorentz Violation is intimately connected with gravity and that LV couplings in QFT must always be fields in a gravitational sector. Diffeomorphism invariance must be intact and the LV couplings transform as tensors under coordinate/frame changes. Therefore searching for LV is one of the most sensitive ways of looking for new physics, either new interactions or modifications of known ones. Energy dissipation/Cerenkov radiation is shown to be a generic feature of LV in QFT. A general computation is done in strongly coupled theories with gravity duals. It is shown that in scale invariant regimes, the energy dissipation rate depends non-triviallly on two characteristic exponents, the Lifshitz exponent and the hyperscaling violation exponent.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We reconsider Lorentz Violation (LV) at the fundamental level. background 0.53 0.72 0.03 unclear 0.75
s1 We show that Lorentz Violation is intimately connected with gravity and that LV couplings in QFT must always be fields in a gravitational sector. result 0.89 0.88 0.61 asserted 1.00
s2 Diffeomorphism invariance must be intact and the LV couplings transform as tensors under coordinate/frame changes. result 0.56 0.25 0.12 asserted 1.00
s3 Therefore searching for LV is one of the most sensitive ways of looking for new physics, either new interactions or modifications of known ones. interpretation 0.99 0.19 0.20 asserted 0.90
s4 Energy dissipation/Cerenkov radiation is shown to be a generic feature of LV in QFT. result 0.99 0.85 0.14 asserted 1.00
s5 A general computation is done in strongly coupled theories with gravity duals. method 0.77 0.90 0.05 asserted 0.94
s6 It is shown that in scale invariant regimes, the energy dissipation rate depends non-triviallly on two characteristic exponents, the Lifshitz exponent and the hyperscaling violation exponent. result 1.00 0.89 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.91.

What was examined, and what was not

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

Figures
Figure 1. Left:gappless generalized Lifshitz geometries in the (z, θ) plane. Right: gapped gener￾alized Lifshitz geometries in the (z, θ) plane. All these geometries pass the Gubser bound tests in (A.5). where the theory is scale invariant albeit in a generic LV fashion. The most general such metric is of the form, [27, 28] ds2 = u θ  − dt2 u2z + b0 du2 + dxidxi u2  (5.12) and is covariant under a generalized Lifshitz scaling symmetry t → λ z t , u → λu , xi → λxi , ds2 → λ −θ ds2 (5.13) with dynamical exponent z. The exponent θ controls the transformation of the metric and is
Figure 2. The trailing string profile. Since S does not depend on ξ but only its derivative, the conjugate momentum πξ is conserved, πξ = − 1 2πℓ2 s b 2 (r)f(r)ξ ′ (r) q 1 − v 2 f(r) + f(r)ξ ′2(r) (6.8) from which we obtain ξ ′ (r) = C f(r) s f(r) − v 2 b 4(r)f(r) − C2 , C = 2πℓ2 sπξ (6.9) The constant C is fixed by the following argument: the numerator inside the square root of (6.8) changes sign and becomes negative at r = rs where f(rs) = v 2 (6.10) The denominator will change sign at some other radial position for arbitrary C. For the solution to be well defined
Figure 3. Left: A plot of the function L M = v z−θ z−2 F[z, θ; v − θ−2 z−2 ] as function of 1 < z < 2 at θ = 0. Right: the same function for z > 2 at θ = 0. In figure 3 we plot the function Lz,θ M = v z−θ z−2F[z, θ; v − θ−2 z−2 ] as function of v, with no hyperscaling violation θ = 0, for different values of z > 1. In all cases Lz,θ asymptotes to a constant as v → 0 while it decreases monotonically and vanishes as v → ∞. Details of the asymptortic expansions can be found at appendix A. The transverse and longitudinal effective masses in (7.18) are plotted in figure 4 for 1 < z < 2, θ
Figure 4. Left:A simultaneous plot of L M , M|| and M⊥ at z = 1.3. Right: the same plot for z = 1.8. 7.2 The holographic computation of the diffusion constants To compute the diffusion coefficients we must compute the real time corelators of the force. We will use holography to compute them. As the string fluctuations are coupled by definition to the medium force, the holographic computation of the force correlators inbvolves the study of the solution of the string fluctuations to quadratic order according to the standard holographic dictionary. We therefore consider quadratic fluctuations…
Figure 5. Left:A simultaneous plot of L M , M|| and M⊥ at z = 2.1. Right: the same plot for z = 8. – 33 –
Figure 6. Left:A simultaneous plot of L M , M|| and M⊥ at θ = 3, z = 5 2 . with Hαβ =
Figure 7. Left:A simultaneous plot of L M , M|| and M⊥ at θ = 3, z = 1 2 . Right: A simultaneous plot of L M , M|| and M⊥ at θ = 3, z = −2. – 34 –
Figure 8. Left:generalized Lifshitz geometries in the (z, θ) plane with θ−2 z−2 > 1 and z−1 z−2 > 0. Right: generalized Lifshitz geometries in the (z, θ) plane with θ−2 z−2 < 1 2 kai z−1 z−2 < 0. – 39 –
Figure 9. Left:generalized Lifshitz geometries in the (z, θ) plane with θ−2 z−2 < 0. All the allowed geometries have z−1 z−2 > 0. and we obtain v → 0 , Lθ,z(v) ≃ M θ−2 z−2 − 1  1 − 1 2 1 − (θ−2) z−2 1 − (θ−2) z−2 +
Figure 10. Plots of the allowed generalized Lifshitz geometries (blue), and regions where (2−z−θ) (z−1) > 0 (purple). In the purple allowed regions (overlap blue+purple), the Langevin evolution is Markov at low velocities. In the blue regions only, the process is Markov only at high velocities. Left figure: The region of case (1a) in appendix A. Middle figure: The region of case (2a) in appendix A. Right figure: The region of case (2a) in appendix A. – 42 –

Figures reproduced from arXiv:1207.2325 by the authors.

References
How the literature uses it

34 arXiv papers cite this in 39 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 · 22 sentences without a confident label

Cites it as background 15 papers

What it cites · 1 sentence without a confident label

Cites as background 1 paper

Discussion

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