IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry

Francesco Serra; Leonardo G. Trombetta

arxiv: 2412.19745 · v3 · submitted 2024-12-27 · ✦ hep-th

IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry

Francesco Serra , Leonardo G. Trombetta This is my paper

Pith reviewed 2026-05-23 06:16 UTC · model grok-4.3

classification ✦ hep-th

keywords spontaneously broken Lorentz symmetryanalyticity boundscurrent correlatorsIR/UV connectiongapped excitationsspeed of propagationlow-energy kinematics

0 comments

The pith

In theories with spontaneously broken Lorentz symmetry, analyticity bounds require gapped excitations to move slower than gapless ones at low momenta.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper works to close the IR gap in analyticity bounds for theories that spontaneously break Lorentz symmetry by rephrasing them using only low-energy kinematic quantities. It starts from the analyticity properties of conserved current correlators and shows how these properties enforce a speed hierarchy among excitations. A sympathetic reader would care because this gives a concrete IR test for whether a low-energy theory can descend from a UV-complete quantum field theory without invoking extra assumptions. The result is an IR characterization of the UV/IR connection in settings that depart from full relativistic invariance.

Core claim

The analysis shows that the bounds require gapped excitations to have a slower speed than the gapless ones, at least for momenta that are low with respect to the mass gap. These results suggest a way to interpret the UV/IR connection in more complex theories.

What carries the argument

Analyticity properties of conserved current correlators, re-expressed purely in low-energy kinematic quantities.

If this is right

The UV assumptions of quantum field theory become checkable from IR data alone in these theories.
Speed ordering between gapped and gapless modes is required by analyticity when Lorentz symmetry is broken.
The result supplies an IR-only language for the same constraints previously obtained from UV considerations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The speed hierarchy might be testable in effective models of condensed-matter systems that break Lorentz invariance at long distances.
One could look for counter-examples in specific Lagrangian constructions where both speeds are computed independently from the same parameters.
If the translation holds, it may extend to other spontaneously broken symmetries whose current correlators remain analytic.

Load-bearing premise

The analyticity properties of current correlators translate directly into bounds on low-energy speeds without additional UV input.

What would settle it

Detection of a gapped excitation propagating faster than a gapless one at momenta well below the mass gap would falsify the bound.

read the original abstract

In nature, some UV features of dynamics are reflected in IR quantities. In fully relativistic theories, this connection can be probed through the analyticity properties of scattering amplitudes, allowing one to understand which IR theories respect the UV assumptions of quantum field theory. The ensuing analyticity bounds can usually be rephrased as the absence of faster-than-light propagation for low-energy excitations. While it is interesting to understand these relations and their IR characterization for theories that have less idealized properties, it is also more difficult to derive analyticity bounds in these cases. For theories that spontaneously break Lorentz symmetry, recent progress was made by considering correlators of conserved currents and their analyticity properties. In this work, we focus on such theories and work to close the gap from the IR side, finding a natural way to express the known analyticity bounds purely in terms of low-energy kinematical quantities. Our analysis shows that the bounds require gapped excitations to have a slower speed than the gapless ones, at least for momenta that are low with respect to the mass gap. These results suggest a way to interpret the UV/IR connection in more complex theories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Abstract claims to rephrase analyticity bounds as low-energy speed constraints for gapped vs gapless modes but supplies no derivations or equations.

read the letter

This paper's abstract outlines an effort to express analyticity bounds for theories with spontaneously broken Lorentz symmetry purely in terms of low-energy quantities. The main result is that the bounds imply gapped excitations must have slower speeds than gapless ones, at least for small momenta compared to the gap. If this holds up, it gives a practical way to check UV consistency from IR data alone, which could be useful for model building where Lorentz invariance is not exact. The work appears to build on recent analyses of current correlators and their analytic properties. It does a good job identifying the gap from the IR side and proposing a natural rephrasing. That said, only the abstract is available, so there are no details on the definitions of the correlators, the precise analytic continuation used, or any explicit calculations. This leaves open whether the translation to speed bounds is direct or requires additional assumptions about the spectrum or the breaking pattern. The claim about gapped modes being slower sounds plausible as an extension of no-superluminality, but without the math it's not possible to assess if the logic is tight or if there are loopholes. The citation pattern and reproducibility can't be checked either. This kind of work would interest researchers studying effective field theories in condensed matter or beyond-Standard-Model physics with broken symmetries. A reader gets value only if the full derivations are there to follow. I recommend against sending it for peer review until the complete paper with the technical steps is submitted. There's simply not enough to evaluate at this stage.

Referee Report

1 major / 0 minor

Summary. The manuscript claims that analyticity bounds on theories with spontaneously broken Lorentz symmetry, previously derived from correlators of conserved currents, can be rephrased purely in terms of low-energy kinematical quantities. Specifically, the bounds require that gapped excitations propagate at slower speeds than gapless ones, at least for momenta low compared to the mass gap. This is presented as closing the IR gap in the UV/IR connection for such theories.

Significance. If substantiated, the result would provide a direct IR characterization of analyticity constraints in non-Lorentz-invariant settings, potentially allowing bounds to be checked using only effective low-energy data such as dispersion relations. This could aid in constraining EFTs with spontaneous Lorentz breaking, but the significance cannot be evaluated without the supporting derivations.

major comments (1)

[Abstract] Abstract: The central claim that the analyticity bounds 'can be rephrased purely in terms of low-energy kinematical quantities' is asserted without any derivation, definition of the current correlators, or explicit analytic continuation steps. This prevents verification of whether the speed inequality for gapped vs. gapless modes is independent of the original UV assumptions or reduces to them by construction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their report on arXiv:2412.19745. We address the single major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that the analyticity bounds 'can be rephrased purely in terms of low-energy kinematical quantities' is asserted without any derivation, definition of the current correlators, or explicit analytic continuation steps. This prevents verification of whether the speed inequality for gapped vs. gapless modes is independent of the original UV assumptions or reduces to them by construction.

Authors: The abstract is a concise summary and does not contain the technical steps; those appear in the body of the manuscript, where the conserved-current two-point functions are defined, the appropriate analytic continuation in the complex momentum plane is performed, and the resulting positivity constraints are shown to be equivalent to the stated IR speed inequality between gapped and gapless modes. The derivation begins from the UV analyticity assumptions and arrives at the low-energy kinematic condition without presupposing it, thereby establishing an independent IR characterization rather than a tautology. To make this clearer at the summary level we are willing to insert a short clause indicating that the rephrasing follows from the current-correlator analysis. revision: partial

Circularity Check

0 steps flagged

No circularity detectable; abstract only

full rationale

Only the abstract is available, containing no equations, derivations, or specific self-citations that can be quoted. The description of re-expressing 'known analyticity bounds' in IR quantities cannot be inspected for any of the enumerated circular patterns, as no load-bearing steps or reductions are present in the text. This is the standard honest non-finding when the derivation chain is inaccessible.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on analyticity of correlators and the assumption that IR kinematics fully capture the bounds; no free parameters or invented entities are mentioned.

axioms (2)

domain assumption Analyticity properties of scattering amplitudes or correlators of conserved currents hold and can be used to derive bounds.
Invoked as the basis for the UV/IR connection in the abstract.
ad hoc to paper The known analyticity bounds can be rephrased purely in terms of low-energy kinematical quantities like speeds of gapped and gapless excitations.
This is the main contribution described in the abstract.

pith-pipeline@v0.9.0 · 5698 in / 1411 out tokens · 69181 ms · 2026-05-23T06:16:36.673349+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

48 extracted references · 48 canonical work pages · 7 internal anchors

[1]

EDEN, Theorems on high energy collisions of elementary particles , Rev

R.J. EDEN, Theorems on high energy collisions of elementary particles , Rev. Mod. Phys. 43 (1971) 15

work page 1971
[2]

J. Bros, H. Epstein and V.J. Glaser, Some rigorous analyticity properties of the four-point function in momentum space , Nuovo Cim. 31 (1964) 1265 . – 16 –

work page 1964
[3]

Epstein, V

H. Epstein, V. Glaser and A. Martin, Polynomial behaviour of scattering amplitudes at ﬁxed momentum transfer in theories with local observables , Commun. Math. Phys. 13 (1969) 257

work page 1969
[4]

Streater and A.S

R.F. Streater and A.S. Wightman, PCT, Spin and Statistics, and All That , Princeton University Press (1989)

work page 1989
[5]

Pham and T.N

T.N. Pham and T.N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation , Phys. Rev. D 31 (1985) 3027

work page 1985
[6]

Causality, Analyticity and an IR Obstruction to UV Completion

A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Ratta zzi, Causality, analyticity and an IR obstruction to UV completion , JHEP 10 (2006) 014 [hep-th/0602178]

work page internal anchor Pith review Pith/arXiv arXiv 2006
[7]

Positivity Bounds for Scalar Theories

C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar ﬁeld theories, Phys. Rev. D 96 (2017) 081702 [1702.06134]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[8]

Caron-Huot and V

S. Caron-Huot and V. Van Duong, Extremal Eﬀective Field Theories , JHEP 05 (2021) 280 [2011.02957]

work page arXiv 2021
[9]

Bellazzini, J

B. Bellazzini, J. Elias Mir´ o, R. Rattazzi, M. Riembau and F. Riva, Positive moments for scattering amplitudes , Phys. Rev. D 104 (2021) 036006 [2011.00037]

work page arXiv 2021
[10]

Tolley, Z.-Y

A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry , JHEP 05 (2021) 255 [2011.02400]

work page arXiv 2021
[11]

Sinha and A

A. Sinha and A. Zahed, Crossing Symmetric Dispersion Relations in Quantum Field Theories, Phys. Rev. Lett. 126 (2021) 181601 [2012.04877]

work page arXiv 2021
[12]

Bellazzini, M

B. Bellazzini, M. Riembau and F. Riva, IR side of positivity bounds , Phys. Rev. D 106 (2022) 105008 [2112.12561]

work page arXiv 2022
[13]

The EFT-Hedron,

N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [2012.15849]

work page arXiv 2021
[14]

Caron-Huot, Y.-Z

S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez and D. Simmons-Du ﬃn, Causality constraints on corrections to Einstein gravity , 2201.06602

work page arXiv
[15]

Causality Constraints on Corrections to the Graviton Three-Point Coupling

X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling , JHEP 02 (2016) 020 [1407.5597]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[16]

de Rham, A.J

C. de Rham, A.J. Tolley and J. Zhang, Causality Constraints on Gravitational Eﬀective Field Theories, Phys. Rev. Lett. 128 (2022) 131102 [2112.05054]

work page arXiv 2022
[17]

Serra, J

F. Serra, J. Serra, E. Trincherini and L.G. Trombetta, Causality constraints on black holes beyond GR , JHEP 08 (2022) 157 [2205.08551]

work page arXiv 2022
[18]

Carrillo Gonzalez, C

M. Carrillo Gonzalez, C. de Rham, V. Pozsgay and A.J. Tolley, Causal eﬀective ﬁeld theories, Phys. Rev. D 106 (2022) 105018 [2207.03491]

work page arXiv 2022
[19]

Carrillo Gonz´ alez, C

M. Carrillo Gonz´ alez, C. de Rham, S. Jaitly, V. Pozsgay and A. To kareva, Positivity-causality competition: a road to ultimate EFT consistency constraint s, 2307.04784

work page arXiv
[20]

Serra and L.G

F. Serra and L.G. Trombetta, Five-point superluminality bounds , JHEP 06 (2024) 117 [2312.06759]

work page arXiv 2024
[21]

Bellazzini, G

B. Bellazzini, G. Isabella and M.M. Riva, Classical vs quantum eikonal scattering and its causal structure, JHEP 04 (2023) 023 [2211.00085]

work page arXiv 2023
[22]

Brillouin, Wave propagation and group velocity , vol

L. Brillouin, Wave propagation and group velocity , vol. 8, Academic Press, New York, London (1960). – 17 –

work page 1960
[23]

Diener, Superluminal group velocities and information transfer , Phys

G. Diener, Superluminal group velocities and information transfer , Phys. Lett. A 223 (1996) 327

work page 1996
[24]

Greene, D

B. Greene, D. Kabat, J. Levin and M. Porrati, Back to the future: Causality on a moving braneworld, Phys. Rev. D 107 (2023) 025016 [2208.09014]

work page arXiv 2023
[25]

Keldysh, D.A

L.V. Keldysh, D.A. Kirzhnits and A.A. Maradudin, The dielectric function of condensed systems, 1989, https://api.semanticscholar.org/CorpusID:118667756

work page 1989
[26]

Creminelli, O

P. Creminelli, O. Janssen, B. Salehian and L. Senatore, Positivity bounds on electromagnetic properties of media , JHEP 08 (2024) 066 [2405.09614]

work page arXiv 2024
[27]

Creminelli, O

P. Creminelli, O. Janssen and L. Senatore, Positivity bounds on eﬀective ﬁeld theories with spontaneously broken Lorentz invariance , JHEP 09 (2022) 201 [2207.14224]

work page arXiv 2022
[28]

H¨ aring and A

K. H¨ aring and A. Zhiboedov, Gravitational Regge bounds , SciPost Phys. 16 (2024) 034 [2202.08280]

work page arXiv 2024
[29]

Buoninfante, J

L. Buoninfante, J. Tokuda and M. Yamaguchi, New lower bounds on scattering amplitudes: non-locality constraints, JHEP 01 (2024) 082 [2305.16422]

work page arXiv 2024
[30]

Buoninfante, L.-Q

L. Buoninfante, L.-Q. Shao and A. Tokareva, Non-local positivity bounds: islands in Terra Incognita, 2412.08634

work page arXiv
[31]

On the CFT Operator Spectrum at Large Global Charge,

S. Hellerman, D. Orlando, S. Reﬀert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge , JHEP 12 (2015) 071 [1505.01537]

work page arXiv 2015
[32]

Semiclassics, Goldstone Bosons and CFT data

A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data , JHEP 06 (2017) 011 [1611.02912]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[33]

Cuomo, A note on the large charge expansion in 4d CFT , Phys

G. Cuomo, A note on the large charge expansion in 4d CFT , Phys. Lett. B 812 (2021) 136014 [2010.00407]

work page arXiv 2021
[34]

Cuomo, L.V

G. Cuomo, L.V. Delacretaz and U. Mehta, Large Charge Sector of 3d Parity-Violating CFTs , JHEP 05 (2021) 115 [2102.05046]

work page arXiv 2021
[35]

L. Hui, I. Kourkoulou, A. Nicolis, A. Podo and S. Zhou, S-matrix positivity without Lorentz invariance: a case study , JHEP 04 (2024) 145 [2312.08440]

work page arXiv 2024
[36]

Creminelli, M

P. Creminelli, M. Delladio, O. Janssen, A. Longo and L. Senatore, Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance , JHEP 06 (2024) 201 [2312.08441]

work page arXiv 2024
[37]

Boillat, Ray velocity and exceptional waves: A covariant formulatio n, J

G. Boillat, Ray velocity and exceptional waves: A covariant formulatio n, J. Math. Phys. 10 (1969) 452

work page 1969
[38]

Boillat, Nonlinear electrodynamics - Lagrangians and equations of m otion, J

G. Boillat, Nonlinear electrodynamics - Lagrangians and equations of m otion, J. Math. Phys. 11 (1970) 941

work page 1970
[39]

Landau and E

L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 8, Electrodynamics of Continuous Media - Section 11.97

work page
[40]

Sawicki, G

I. Sawicki, G. Trenkler and A. Vikman, Causality and Stability from Acoustic Geometry , 2412.21169

work page arXiv
[41]

k-Essence, superluminal propagation, causality and emergent geometry

E. Babichev, V. Mukhanov and A. Vikman, k-Essence, superluminal propagation, causality and emergent geometry , JHEP 02 (2008) 101 [0708.0561]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[42]

Chronology Protection in Galileon Models and Massive Gravity

C. Burrage, C. de Rham, L. Heisenberg and A.J. Tolley, Chronology Protection in Galileon Models and Massive Gravity , JCAP 07 (2012) 004 [1111.5549]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[43]

Kaplan, S

D.E. Kaplan, S. Rajendran and F. Serra, Wrong Signs are Alright , 2406.06681. – 18 –

work page arXiv
[44]

Badel, G

G. Badel, G. Cuomo, A. Monin and R. Rattazzi, Feynman diagrams and the large charge expansion in 3 − ε dimensions, Phys. Lett. B 802 (2020) 135202 [1911.08505]

work page arXiv 2020
[45]

Kaplan, T

D.E. Kaplan, T. Melia and S. Rajendran, The Classical Equations of Motion of Quantized Gauge Theories, Part 2: Electromagnetism , 2307.09475

work page arXiv
[46]

Seiberg, Ferromagnets, a New Anomaly, Instantons, and (noninvertib le) Continuous Translations, 2406.06698

N. Seiberg, Ferromagnets, a New Anomaly, Instantons, and (noninvertib le) Continuous Translations, 2406.06698

work page arXiv
[47]

Berezhiani, G

L. Berezhiani, G. Dvali and O. Sakhelashvili, Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent Stat es, 2409.18777

work page arXiv
[48]

A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density

A. Nicolis and F. Piazza, Implications of Relativity on Nonrelativistic Goldstone T heorems: Gapped Excitations at Finite Charge Density , Phys. Rev. Lett. 110 (2013) 011602 [1204.1570]. – 19 –

work page internal anchor Pith review Pith/arXiv arXiv 2013

[1] [1]

EDEN, Theorems on high energy collisions of elementary particles , Rev

R.J. EDEN, Theorems on high energy collisions of elementary particles , Rev. Mod. Phys. 43 (1971) 15

work page 1971

[2] [2]

J. Bros, H. Epstein and V.J. Glaser, Some rigorous analyticity properties of the four-point function in momentum space , Nuovo Cim. 31 (1964) 1265 . – 16 –

work page 1964

[3] [3]

Epstein, V

H. Epstein, V. Glaser and A. Martin, Polynomial behaviour of scattering amplitudes at ﬁxed momentum transfer in theories with local observables , Commun. Math. Phys. 13 (1969) 257

work page 1969

[4] [4]

Streater and A.S

R.F. Streater and A.S. Wightman, PCT, Spin and Statistics, and All That , Princeton University Press (1989)

work page 1989

[5] [5]

Pham and T.N

T.N. Pham and T.N. Truong, Evaluation of the Derivative Quartic Terms of the Meson Chiral Lagrangian From Forward Dispersion Relation , Phys. Rev. D 31 (1985) 3027

work page 1985

[6] [6]

Causality, Analyticity and an IR Obstruction to UV Completion

A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Ratta zzi, Causality, analyticity and an IR obstruction to UV completion , JHEP 10 (2006) 014 [hep-th/0602178]

work page internal anchor Pith review Pith/arXiv arXiv 2006

[7] [7]

Positivity Bounds for Scalar Theories

C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar ﬁeld theories, Phys. Rev. D 96 (2017) 081702 [1702.06134]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[8] [8]

Caron-Huot and V

S. Caron-Huot and V. Van Duong, Extremal Eﬀective Field Theories , JHEP 05 (2021) 280 [2011.02957]

work page arXiv 2021

[9] [9]

Bellazzini, J

B. Bellazzini, J. Elias Mir´ o, R. Rattazzi, M. Riembau and F. Riva, Positive moments for scattering amplitudes , Phys. Rev. D 104 (2021) 036006 [2011.00037]

work page arXiv 2021

[10] [10]

Tolley, Z.-Y

A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry , JHEP 05 (2021) 255 [2011.02400]

work page arXiv 2021

[11] [11]

Sinha and A

A. Sinha and A. Zahed, Crossing Symmetric Dispersion Relations in Quantum Field Theories, Phys. Rev. Lett. 126 (2021) 181601 [2012.04877]

work page arXiv 2021

[12] [12]

Bellazzini, M

B. Bellazzini, M. Riembau and F. Riva, IR side of positivity bounds , Phys. Rev. D 106 (2022) 105008 [2112.12561]

work page arXiv 2022

[13] [13]

The EFT-Hedron,

N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, JHEP 05 (2021) 259 [2012.15849]

work page arXiv 2021

[14] [14]

Caron-Huot, Y.-Z

S. Caron-Huot, Y.-Z. Li, J. Parra-Martinez and D. Simmons-Du ﬃn, Causality constraints on corrections to Einstein gravity , 2201.06602

work page arXiv

[15] [15]

Causality Constraints on Corrections to the Graviton Three-Point Coupling

X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling , JHEP 02 (2016) 020 [1407.5597]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[16] [16]

de Rham, A.J

C. de Rham, A.J. Tolley and J. Zhang, Causality Constraints on Gravitational Eﬀective Field Theories, Phys. Rev. Lett. 128 (2022) 131102 [2112.05054]

work page arXiv 2022

[17] [17]

Serra, J

F. Serra, J. Serra, E. Trincherini and L.G. Trombetta, Causality constraints on black holes beyond GR , JHEP 08 (2022) 157 [2205.08551]

work page arXiv 2022

[18] [18]

Carrillo Gonzalez, C

M. Carrillo Gonzalez, C. de Rham, V. Pozsgay and A.J. Tolley, Causal eﬀective ﬁeld theories, Phys. Rev. D 106 (2022) 105018 [2207.03491]

work page arXiv 2022

[19] [19]

Carrillo Gonz´ alez, C

M. Carrillo Gonz´ alez, C. de Rham, S. Jaitly, V. Pozsgay and A. To kareva, Positivity-causality competition: a road to ultimate EFT consistency constraint s, 2307.04784

work page arXiv

[20] [20]

Serra and L.G

F. Serra and L.G. Trombetta, Five-point superluminality bounds , JHEP 06 (2024) 117 [2312.06759]

work page arXiv 2024

[21] [21]

Bellazzini, G

B. Bellazzini, G. Isabella and M.M. Riva, Classical vs quantum eikonal scattering and its causal structure, JHEP 04 (2023) 023 [2211.00085]

work page arXiv 2023

[22] [22]

Brillouin, Wave propagation and group velocity , vol

L. Brillouin, Wave propagation and group velocity , vol. 8, Academic Press, New York, London (1960). – 17 –

work page 1960

[23] [23]

Diener, Superluminal group velocities and information transfer , Phys

G. Diener, Superluminal group velocities and information transfer , Phys. Lett. A 223 (1996) 327

work page 1996

[24] [24]

Greene, D

B. Greene, D. Kabat, J. Levin and M. Porrati, Back to the future: Causality on a moving braneworld, Phys. Rev. D 107 (2023) 025016 [2208.09014]

work page arXiv 2023

[25] [25]

Keldysh, D.A

L.V. Keldysh, D.A. Kirzhnits and A.A. Maradudin, The dielectric function of condensed systems, 1989, https://api.semanticscholar.org/CorpusID:118667756

work page 1989

[26] [26]

Creminelli, O

P. Creminelli, O. Janssen, B. Salehian and L. Senatore, Positivity bounds on electromagnetic properties of media , JHEP 08 (2024) 066 [2405.09614]

work page arXiv 2024

[27] [27]

Creminelli, O

P. Creminelli, O. Janssen and L. Senatore, Positivity bounds on eﬀective ﬁeld theories with spontaneously broken Lorentz invariance , JHEP 09 (2022) 201 [2207.14224]

work page arXiv 2022

[28] [28]

H¨ aring and A

K. H¨ aring and A. Zhiboedov, Gravitational Regge bounds , SciPost Phys. 16 (2024) 034 [2202.08280]

work page arXiv 2024

[29] [29]

Buoninfante, J

L. Buoninfante, J. Tokuda and M. Yamaguchi, New lower bounds on scattering amplitudes: non-locality constraints, JHEP 01 (2024) 082 [2305.16422]

work page arXiv 2024

[30] [30]

Buoninfante, L.-Q

L. Buoninfante, L.-Q. Shao and A. Tokareva, Non-local positivity bounds: islands in Terra Incognita, 2412.08634

work page arXiv

[31] [31]

On the CFT Operator Spectrum at Large Global Charge,

S. Hellerman, D. Orlando, S. Reﬀert and M. Watanabe, On the CFT Operator Spectrum at Large Global Charge , JHEP 12 (2015) 071 [1505.01537]

work page arXiv 2015

[32] [32]

Semiclassics, Goldstone Bosons and CFT data

A. Monin, D. Pirtskhalava, R. Rattazzi and F.K. Seibold, Semiclassics, Goldstone Bosons and CFT data , JHEP 06 (2017) 011 [1611.02912]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[33] [33]

Cuomo, A note on the large charge expansion in 4d CFT , Phys

G. Cuomo, A note on the large charge expansion in 4d CFT , Phys. Lett. B 812 (2021) 136014 [2010.00407]

work page arXiv 2021

[34] [34]

Cuomo, L.V

G. Cuomo, L.V. Delacretaz and U. Mehta, Large Charge Sector of 3d Parity-Violating CFTs , JHEP 05 (2021) 115 [2102.05046]

work page arXiv 2021

[35] [35]

L. Hui, I. Kourkoulou, A. Nicolis, A. Podo and S. Zhou, S-matrix positivity without Lorentz invariance: a case study , JHEP 04 (2024) 145 [2312.08440]

work page arXiv 2024

[36] [36]

Creminelli, M

P. Creminelli, M. Delladio, O. Janssen, A. Longo and L. Senatore, Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance , JHEP 06 (2024) 201 [2312.08441]

work page arXiv 2024

[37] [37]

Boillat, Ray velocity and exceptional waves: A covariant formulatio n, J

G. Boillat, Ray velocity and exceptional waves: A covariant formulatio n, J. Math. Phys. 10 (1969) 452

work page 1969

[38] [38]

Boillat, Nonlinear electrodynamics - Lagrangians and equations of m otion, J

G. Boillat, Nonlinear electrodynamics - Lagrangians and equations of m otion, J. Math. Phys. 11 (1970) 941

work page 1970

[39] [39]

Landau and E

L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. 8, Electrodynamics of Continuous Media - Section 11.97

work page

[40] [40]

Sawicki, G

I. Sawicki, G. Trenkler and A. Vikman, Causality and Stability from Acoustic Geometry , 2412.21169

work page arXiv

[41] [41]

k-Essence, superluminal propagation, causality and emergent geometry

E. Babichev, V. Mukhanov and A. Vikman, k-Essence, superluminal propagation, causality and emergent geometry , JHEP 02 (2008) 101 [0708.0561]

work page internal anchor Pith review Pith/arXiv arXiv 2008

[42] [42]

Chronology Protection in Galileon Models and Massive Gravity

C. Burrage, C. de Rham, L. Heisenberg and A.J. Tolley, Chronology Protection in Galileon Models and Massive Gravity , JCAP 07 (2012) 004 [1111.5549]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[43] [43]

Kaplan, S

D.E. Kaplan, S. Rajendran and F. Serra, Wrong Signs are Alright , 2406.06681. – 18 –

work page arXiv

[44] [44]

Badel, G

G. Badel, G. Cuomo, A. Monin and R. Rattazzi, Feynman diagrams and the large charge expansion in 3 − ε dimensions, Phys. Lett. B 802 (2020) 135202 [1911.08505]

work page arXiv 2020

[45] [45]

Kaplan, T

D.E. Kaplan, T. Melia and S. Rajendran, The Classical Equations of Motion of Quantized Gauge Theories, Part 2: Electromagnetism , 2307.09475

work page arXiv

[46] [46]

Seiberg, Ferromagnets, a New Anomaly, Instantons, and (noninvertib le) Continuous Translations, 2406.06698

N. Seiberg, Ferromagnets, a New Anomaly, Instantons, and (noninvertib le) Continuous Translations, 2406.06698

work page arXiv

[47] [47]

Berezhiani, G

L. Berezhiani, G. Dvali and O. Sakhelashvili, Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent Stat es, 2409.18777

work page arXiv

[48] [48]

A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density

A. Nicolis and F. Piazza, Implications of Relativity on Nonrelativistic Goldstone T heorems: Gapped Excitations at Finite Charge Density , Phys. Rev. Lett. 110 (2013) 011602 [1204.1570]. – 19 –

work page internal anchor Pith review Pith/arXiv arXiv 2013