Abstract
We revisit here the naturalness problem of Lorentz invariance violations on a simple toy model of a scalar field coupled to a fermion field via a Yukawa interaction. We first review some well-known results concerning the low-energy percolation of Lorentz violation from high energies, presenting some details of the analysis not explicitly discussed in the literature and discussing some previously unnoticed subtleties. We then show how a separation between the scale of validity of the effective field theory and that one of Lorentz invariance violations can hinder this low-energy percolation. While such protection mechanism was previously considered in the literature, we provide here a simple illustration of how it works and of its general features. Finally, we consider a case in which dissipation is present, showing that the dissipative behaviour does not percolate generically to lower mass dimension operators albeit dispersion does. Moreover, we show that a scale separation can protect from unsuppressed low-energy percolation also in this case.
References
S. Liberati, Tests of Lorentz invariance: a 2013 update, Class. Quant. Grav. 30 (2013) 133001 [arXiv:1304.5795] [INSPIRE].
D. Mattingly, Modern tests of Lorentz invariance, Living Rev. Rel. 8 (2005) 5 [gr-qc/0502097] [INSPIRE].
G. Amelino-Camelia, Quantum-spacetime phenomenology, Living Rev. Rel. 16 (2013) 5 [arXiv:0806.0339] [INSPIRE].
M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [INSPIRE].
R. Gambini and J. Pullin, Nonstandard optics from quantum space-time, Phys. Rev. D 59 (1999) 124021 [gr-qc/9809038] [INSPIRE].
L.F. Urrutia, Corrections to flat-space particle dynamics arising from space granularity, Lect. Notes Phys. 702 (2006) 299 [hep-ph/0506260] [INSPIRE].
N.E. Mavromatos, Lorentz invariance violation from string theory, PoS(QG-Ph)027 [arXiv:0708.2250] [INSPIRE].
P. Hořava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [INSPIRE].
T. Jacobson, Einstein-aether gravity: a status report, PoS (QG-Ph) 020 [arXiv:0801.1547] [INSPIRE].
G. Amelino-Camelia, Testable scenario for relativity with minimum length, Phys. Lett. B 510 (2001) 255 [hep-th/0012238] [INSPIRE].
G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman and L. Smolin, The principle of relative locality, Phys. Rev. D 84 (2011) 084010 [arXiv:1101.0931] [INSPIRE].
C. Rovelli and S. Speziale, Lorentz covariance of loop quantum gravity, Phys. Rev. D 83 (2011) 104029 [arXiv:1012.1739] [INSPIRE].
L. Bombelli, J. Lee, D. Meyer and R. Sorkin, Space-time as a causal set, Phys. Rev. Lett. 59 (1987) 521 [INSPIRE].
L. Bombelli, J. Henson and R.D. Sorkin, Discreteness without symmetry breaking: a theorem, Mod. Phys. Lett. A 24 (2009) 2579 [gr-qc/0605006] [INSPIRE].
G. Amelino-Camelia, Relativity in space-times with short distance structure governed by an observer independent (Planckian) length scale, Int. J. Mod. Phys. D 11 (2002) 35 [gr-qc/0012051] [INSPIRE].
J. Collins, A. Perez, D. Sudarsky, L. Urrutia and H. Vucetich, Lorentz invariance and quantum gravity: an additional fine-tuning problem?, Phys. Rev. Lett. 93 (2004) 191301 [gr-qc/0403053] [INSPIRE].
R. Iengo, J.G. Russo and M. Serone, Renormalization group in Lifshitz-type theories, JHEP 11 (2009) 020 [arXiv:0906.3477] [INSPIRE].
R. Gambini, S. Rastgoo and J. Pullin, Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?, Class. Quant. Grav. 28 (2011) 155005 [arXiv:1106.1417] [INSPIRE].
J. Polchinski, Comment on ‘Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?’, Class. Quant. Grav. 29 (2012) 088001 [arXiv:1106.6346] [INSPIRE].
N. Afshordi, Why is high energy physics Lorentz invariant?, arXiv:1511.07879 [INSPIRE].
S. Groot Nibbelink and M. Pospelov, Lorentz violation in supersymmetric field theories, Phys. Rev. Lett. 94 (2005) 081601 [hep-ph/0404271] [INSPIRE].
P.A. Bolokhov, S. Groot Nibbelink and M. Pospelov, Lorentz violating supersymmetric quantum electrodynamics, Phys. Rev. D 72 (2005) 015013 [hep-ph/0505029] [INSPIRE].
L. Sindoni, The Higgs mechanism in Finsler spacetimes, Phys. Rev. D 77 (2008) 124009 [arXiv:0712.3518] [INSPIRE].
M. Pospelov and Y. Shang, On Lorentz violation in Hořava-Lifshitz type theories, Phys. Rev. D 85 (2012) 105001 [arXiv:1010.5249] [INSPIRE].
H.B. Nielsen and M. Ninomiya, β-function in a non-covariant Yang-Mills theory, Nucl. Phys. B 141 (1978) 153 [INSPIRE].
H.B. Nielsen and I. Picek, The Rédei-like model and testing Lorentz invariance, Phys. Lett. B 114 (1982) 141 [INSPIRE].
G. Bednik, O. Pujolàs and S. Sibiryakov, Emergent Lorentz invariance from strong dynamics: holographic examples, JHEP 11 (2013) 064 [arXiv:1305.0011] [INSPIRE].
J. Collins, A. Perez and D. Sudarsky, Lorentz invariance violation and its role in quantum gravity phenomenology, in Approaches to quantum gravity: towards a new understanding of space and time, D. Oriti ed., Cambridge University Press, Cambridge U.K. (2006) [hep-th/0603002] [INSPIRE].
R. Parentani, Constructing QFT’s wherein Lorentz invariance is broken by dissipative effects in the UV, PoS(QG-Ph)031 [arXiv:0709.3943] [INSPIRE].
A. Perez and D. Sudarsky, Comments on challenges for quantum gravity, Phys. Rev. Lett. 91 (2003) 179101 [gr-qc/0306113] [INSPIRE].
J. Alfaro, Quantum gravity and Lorentz invariance deformation in the standard model, Phys. Rev. Lett. 94 (2005) 221302 [hep-th/0412295] [INSPIRE].
R.C. Myers and M. Pospelov, Experimental challenges for quantum gravity, in Proceedings of the 3rd International Symposium on Quantum Theory and Symmetries (QTS-3), Cincinnati U.S.A. (2003), pp. 732-744 [gr-qc/0402028] [INSPIRE].
R.P. Woodard, Ostrogradsky’s theorem on Hamiltonian instability, Scholarpedia 10 (2015) 32243 [arXiv:1506.02210] [INSPIRE].
D.A. Eliezer and R.P. Woodard, The problem of nonlocality in string theory, Nucl. Phys. B 325 (1989) 389 [INSPIRE].
G. Kleppe and R.P. Woodard, Nonlocal Yang-Mills, Nucl. Phys. B 388 (1992) 81 [hep-th/9203016] [INSPIRE].
S.D. Joglekar, Causality violation in non-local QFT, in Workshop Series on Theoretical High Energy Physics, Roorkee India (2005) [hep-th/0601006] [INSPIRE].
L. Modesto and L. Rachwal, Universally finite gravitational and gauge theories, Nucl. Phys. B 900 (2015) 147 [arXiv:1503.00261] [INSPIRE].
E.T. Tomboulis, Nonlocal and quasilocal field theories, Phys. Rev. D 92 (2015) 125037 [arXiv:1507.00981] [INSPIRE].
S.B. Giddings, Locality in quantum gravity and string theory, Phys. Rev. D 74 (2006) 106006 [hep-th/0604072] [INSPIRE].
G. Calcagni and L. Modesto, Nonlocality in string theory, J. Phys. A 47 (2014) 355402 [arXiv:1310.4957] [INSPIRE].
F. Markopoulou and L. Smolin, Disordered locality in loop quantum gravity states, Class. Quant. Grav. 24 (2007) 3813 [gr-qc/0702044] [INSPIRE].
R.D. Sorkin, Does locality fail at intermediate length-scales, in Approaches to quantum gravity: towards a new understanding of space and time, D. Oriti ed., Cambridge University Press, Cambridge U.K. (2006) [gr-qc/0703099] [INSPIRE].
A. Belenchia, D.M.T. Benincasa and S. Liberati, Nonlocal scalar quantum field theory from causal sets, JHEP 03 (2015) 036 [arXiv:1411.6513] [INSPIRE].
R. Gambini and J. Pullin, Emergence of stringlike physics from Lorentz invariance in loop quantum gravity, Int. J. Mod. Phys. D 23 (2014) 1442023 [arXiv:1406.2610] [INSPIRE].
F. Dowker, J. Henson and R.D. Sorkin, Quantum gravity phenomenology, Lorentz invariance and discreteness, Mod. Phys. Lett. A 19 (2004) 1829 [gr-qc/0311055] [INSPIRE].
A. Jain and S.D. Joglekar, Causality violation in nonlocal quantum field theory, Int. J. Mod. Phys. A 19 (2004) 3409 [hep-th/0307208] [INSPIRE].
G. Saini and S.D. Joglekar, Bound on nonlocal scale from g − 2 of muon in a nonlocal W-S model, Z. Phys. C 76 (1997) 343 [hep-ph/9701405] [INSPIRE].
D. Evens, J.W. Moffat, G. Kleppe and R.P. Woodard, Nonlocal regularizations of gauge theories, Phys. Rev. D 43 (1991) 499 [INSPIRE].
D. Sudarsky and J.A. Caicedo, On the proposals of Lorentz invariance violation resulting from a quantum-gravitational granularity of space-time, J. Phys. Conf. Ser. 24 (2005) 69 [INSPIRE].
S. Liberati and L. Maccione, Astrophysical constraints on Planck scale dissipative phenomena, Phys. Rev. Lett. 112 (2014) 151301 [arXiv:1309.7296] [INSPIRE].
E. Borriello, S. Chakraborty, A. Mirizzi and P.D. Serpico, Stringent constraint on neutrino Lorentz-invariance violation from the two IceCube PeV neutrinos, Phys. Rev. D 87 (2013) 116009 [arXiv:1303.5843] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1601.06700
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Belenchia, A., Gambassi, A. & Liberati, S. Lorentz violation naturalness revisited. J. High Energ. Phys. 2016, 49 (2016). https://doi.org/10.1007/JHEP06(2016)049
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2016)049
Keywords
- Space-Time Symmetries
- Effective field theories