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Spontaneous Lorentz Breaking at High Energies

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Hsin-Chia Cheng, Markus A. Luty, Shinji Mukohyama, Jesse Thaler

High Energy Physics - Theory · Submitted 1 Mar 2006 · 59 references

Pith's verdict: Solid EFT paper that moves the ghost condensate program to a vector order parameter and raises the Lorentz-breaking scale; the black-hole accretion bound is the one genuinely shaky leg, but the central high-scale claim survives.

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arXiv IDhep-th/0603010 (version 2)
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CitationHsin-Chia Cheng, Jesse Thaler, Markus A. Luty, Shinji Mukohyama. "Spontaneous Lorentz Breaking at High Energies." arXiv:hep-th/0603010 (2006). https://pith.science/paper/4VHDUGPD
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The paper

The paper claims

Spontaneous Lorentz breaking can reach 10^12 GeV if a vector field does the job.

The reading

The paper's central claim is that spontaneous Lorentz breaking need not be confined to energies near 100 GeV: if the breaking is realized by the vacuum value of a vector field in a theory obtained by gauging the ghost condensate, the scale can be as high as $10^{12}$ GeV while remaining consistent with gravitational and matter experiments. In the minimal scalar ghost condensate, the single Goldstone mode mixes strongly with gravity and causes an infrared (Jeans-like) instability above about 100 GeV. The vector theory adds three degrees of freedom, shields the electric component, and reduces the mixing with the Newtonian potential to a tiny preferred-frame effect. The authors derive the allowed range M < min($10^{12}$ GeV, $g^{2}$ $10^{15}$ GeV), identify a distinctive spin-dependent inverse-square force, and argue that nonlinear dynamics avoids black-hole-accretion singularities that would otherwise invalidate the construction.

What carries the argument

The central object is the gauged ghost condensate: a U(1) gauge field A_mu with a Lorentz-violating vacuum expectation value <A_0> = M, obtained by gauging the shift symmetry of the ghost condensate. The gauge-invariant combination A_mu + M partial_mu phi means the Goldstone mode pi is eaten; only A0 gets a mass while the three spatial components A_i stay massless, so gravity mixes only through derivatives. The load-bearing identity is the scalar-mode speed $c_s^{2}$ = $\alpha$ ($g^{2}$ - $g_c^{2}$), with g_c = M/($\sqrt$(2) M_Pl); positivity is stability and g > g_c suppresses the mixing of the condensate with the Newtonian potential. Nonlinear dynamics is described as a charged fluid whose electric field builds up a repulsive force that makes would-be caustics bounce, except in exactly planar symmetry where fragmentation is expected but not proven.

Extended reading notes

Core claim

The paper establishes that spontaneous Lorentz breaking can occur at scales as high as M lesssim min($10^{12}$ GeV, $g^{2}$ $10^{15}$ GeV), provided the breaking is mediated by a vector field configured as a gauged ghost condensate. In the minimal scalar ghost condensate, mixing with gravity forces an infrared instability above M ~ 100 GeV; gauging the ghost condensate adds three degrees of freedom, shields the electric component A0, and makes the mixing with the Newtonian potential small, so the leading modification is a direction-dependent Newtonian potential with PPN parameter alpha2 ~ $M^{2}$/(2 $\alpha$ $g^{4}$ $M_Pl^{2}$), bounded by 4 x $10^{-7}$. With stability $c_s^{2}$ = $\alpha$ ($g^{2}$ - $g_c^{2}$) > 0, where g_c = M/($\sqrt$(2) M_Pl), the theory has no Jeans-like instability at long wavelengths.

Load-bearing premise

The whole high-scale scenario rests on the claim that the gauged ghost condensate around a black hole settles into a smooth congruence of infalling geodesics without shell-crossing singularities, so the late-time accretion formula used here applies; this is supported by numerical evidence and a fragmentation argument, not by proof.

Editorial extensions

If this is right

  • Lorentz violation can be a high-energy phenomenon tied to fundamental particle physics rather than an infrared artifact; the scale can lie near the intermediate mass scale 10^12 GeV.
  • Gravity remains almost Einsteinian: the only post-Newtonian modification is the preferred-frame parameter alpha2, so solar-system tests constrain M via g^4 but no other PPN parameters are changed.
  • Black-hole accretion of the condensate gives a robust upper bound M lesssim 10^12 GeV (times alpha^-1/2) from stellar-mass black holes, independent of direct matter couplings.
  • If the sector couples to matter only gravitationally, bounds are weaker; if it couples through axial currents, there is a spin-dependent 1/r potential with angular structure that distinguishes it from both electromagnetism and the minimal ghost condensate.
  • Gravitational Cherenkov radiation and anomalous accelerations of the Sun are suppressed enough for M up to roughly 10^10 GeV unless alpha2 bounds intervene, while binary pulsar timing can compete near the sound-speed threshold.

Reading between the lines

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

  • A direct numerical study of perturbed planar collapse could settle whether the fragmentation claim holds: if a planar caustic forms before the effective theory breaks down even with small seed perturbations, the singularity-avoidance argument would need revision.
  • The decoupling limit M -> infinity with g^-2 M^2 and alpha M^2 held fixed maps this model onto constrained preferred-frame vector theories; bounds derived in that limit should therefore be reinterpretable as limits on M and g here, which may allow existing data to sharpen the 10^15 GeV branch.
  • If the axial coupling dominates, the spin-dependent inverse-square potential with the angular structure derived for this model is a distinctive target; a null experiment using a toroidal ferromagnet, which produces no external magnetic field, could probe the coupling at gravitational strength.
Original abstract

Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation value of a vector field. This theory can be constructed by gauging ghost condensation, giving a systematic effective field theory description that allows us to estimate the size of all physical effects. We show that nonlinear effects become important for gravitational fields with strength \sqrt{\Phi} > g, where g is the gauge coupling, and we argue that the nonlinear dynamics is free from singularities. We then analyze the phenomenology of the model, including nonlinear dynamics and velocity-dependent effects. The strongest bounds on the gravitational sector come from either black hole accretion or direction-dependent gravitational forces, and imply that the scale of spontaneous Lorentz breaking is M < Min(10^{12}GeV, g^2 10^{15}GeV). If the Lorentz breaking sector couples directly to matter, there is a spin-dependent inverse-square law force, which has a different angular dependence from the force mediated by the ghost condensate, providing a distinctive signature for this class of models.

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, 6,507 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.80 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation value of a vector field. This theory can be constructed by gauging ghost condensation, giving a systematic effective field theory description that allows us to estimate the size of all physical effects. We show that nonlinear effects become important for gravitational fields with strength \sqrt{\Phi} > g, where g is the gauge coupling, and we argue that the nonlinear dynamics is free from singularities. We then analyze the phenomenology of the model, including nonlinear dynamics and velocity-dependent effects. The strongest bounds on the gravitational sector come from either black hole accretion or direction-dependent gravitational forces, and imply that the scale of spontaneous Lorentz breaking is M < Min(10^{12}GeV, g^2 10^{15}GeV). If the Lorentz breaking sector couples directly to matter, there is a spin-dependent inverse-square law force, which has a different angular dependence from the force mediated by the ghost condensate, providing a distinctive signature for this class of models.

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 Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. background 1.00 0.08 0.06 asserted 0.99
s1 In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. background 0.91 0.13 0.05 asserted 0.97
s2 We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation value of a vector field. result 0.51 0.87 0.72 asserted 0.66
s3 This theory can be constructed by gauging ghost condensation, giving a systematic effective field theory description that allows us to estimate the size of all physical effects. method 0.88 0.82 0.08 asserted 0.92
s4 We show that nonlinear effects become important for gravitational fields with strength \sqrt{\Phi} > g, where g is the gauge coupling, and we argue that the nonlinear dynamics is free from singularities. result 0.96 0.91 0.08 asserted 0.99
s5 We then analyze the phenomenology of the model, including nonlinear dynamics and velocity-dependent effects. contribution 0.89 0.88 0.04 asserted 0.80
s6 The strongest bounds on the gravitational sector come from either black hole accretion or direction-dependent gravitational forces, and imply that the scale of spontaneous Lorentz breaking is M < Min(10^{12}GeV, g^2 10^{15}GeV). result 0.99 0.68 0.34 asserted 0.96
s7 If the Lorentz breaking sector couples directly to matter, there is a spin-dependent inverse-square law force, which has a different angular dependence from the force mediated by the ghost condensate, providing a distinctive signature for this class of models. result 0.76 0.66 0.08 asserted 0.90

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.89.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

Figures
Figure 1. A result of numerical simulation for planar symmetry (s = 0). The variable Ar is plotted as a function of r and t. After an initial bounce, a caustic singularity forms at late times. Note that in a realistic situation, we do not expect a system to exhibit planar symmetry
Figure 2. A result of numerical simulation in cylindrial symmetry (s = 1). The variable Ar is plotted as a function of r and t. After an initial bounce, no caustics form at late times. 22
Figure 3. A result of numerical simulation in spherical symmetry (s = 2). The variable Ar is plotted as a function of r and t. Like the case of cylindrical symmetry, there are no late time caustics
Figure 4. A result of numerical simulation in spherical symmetry (s = 2) with an external gravitational potential. The variable Ar is plotted as a function of r and t. Again, we observe the absence of late time caustics. 23
Figure 5. A result of numerical simulation in spherical symmetry (s = 2) with an external gravitational potential. The variable Er is plotted as a function of r and t. At late times, the “electric field” cancels the gravitational force, halting the accretion of the gauged ghost condensate and protecting the system from caustics. 24

Figures reproduced from arXiv:hep-th/0603010 by the authors.

References
How the literature uses it

29 arXiv papers cite this in 51 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 · 35 sentences without a confident label

Compares with it 1 paper
  • Therefore, the residual symmetries are the spatial diffs and a combination of the $U(1)$ and time diffs [ref], which are exactly the same as the symmetries of the gauged ghost condensate [ref] .

    The Effective Field Theory of Vector-Tensor Theories · Symmetry breaking pattern · 0.84

Cites it as support 1 paper
Cites it as background 14 papers

Discussion

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