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Today one tries to find indications for quantum gravity indirectly via low-energy effects induced by "foamy" or "discrete" structures replacing space-time at the Planck regime. It is by no means clear whether and how such discrete structures necessarily indice Lorentz symmery breaking, neither in the UV, nor in the IR. In addtion it is not clear how such UV effects manifest itslef (indirectly) in the IR.
Therefore the general conclusion that not observing these indirect effects at low energy automatically rule out these "discrete models" in the UV.
Two references regarding the relation of UV and IR effects:
http://arxiv.org/PS_cache/gr-qc/pdf/0403/0403053v4.pdf
Phys.Rev.Lett.93:191301,2004
Lorentz invariance and quantum gravity: an additional fine-tuning problem?
John Collins, Alejandro Perez, Daniel Sudarsky, Luis Urrutia, Héctor Vucetich
(Submitted on 12 Mar 2004 (v1), last revised 30 Oct 2004 (this version, v4))
Abstract: Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the theory are unnaturally strongly fine-tuned. Therefore an important task is not just the improvement of the precision of searches for violations of Lorentz invariance, but also the search for theoretical mechanisms for automatically preserving Lorentz invariance.
http://arxiv.org/abs/1106.6346v2
Comment on http://arxiv.org/abs/1106.1417" "Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?"
Joseph Polchinski
(Submitted on 30 Jun 2011 (v1), last revised 2 Sep 2011 (this version, v2))
Abstract: A recent paper by Gambini, Rastgoo and Pullin [arXiv:1106.1417 investigates the important issue of constraints from Lorentz invariance on Planck scale physics, arguing that the classic analysis of Collins, Perez, Sudarsky, Urrutia and Vucetich \cite{cpsuv} is not generally valid. We argue that the new work is based on models that do not capture the relevant physics, and that almost all models of observable high energy Lorentz violation, and proposed Lorentz-violating theories of quantum gravity, are ruled out by low energy tests; the only known exceptions are based on supersymmetry.
Therefore the general conclusion that not observing these indirect effects at low energy automatically rule out these "discrete models" in the UV.
Two references regarding the relation of UV and IR effects:
http://arxiv.org/PS_cache/gr-qc/pdf/0403/0403053v4.pdf
Phys.Rev.Lett.93:191301,2004
Lorentz invariance and quantum gravity: an additional fine-tuning problem?
John Collins, Alejandro Perez, Daniel Sudarsky, Luis Urrutia, Héctor Vucetich
(Submitted on 12 Mar 2004 (v1), last revised 30 Oct 2004 (this version, v4))
Abstract: Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the theory are unnaturally strongly fine-tuned. Therefore an important task is not just the improvement of the precision of searches for violations of Lorentz invariance, but also the search for theoretical mechanisms for automatically preserving Lorentz invariance.
http://arxiv.org/abs/1106.6346v2
Comment on http://arxiv.org/abs/1106.1417" "Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?"
Joseph Polchinski
(Submitted on 30 Jun 2011 (v1), last revised 2 Sep 2011 (this version, v2))
Abstract: A recent paper by Gambini, Rastgoo and Pullin [arXiv:1106.1417 investigates the important issue of constraints from Lorentz invariance on Planck scale physics, arguing that the classic analysis of Collins, Perez, Sudarsky, Urrutia and Vucetich \cite{cpsuv} is not generally valid. We argue that the new work is based on models that do not capture the relevant physics, and that almost all models of observable high energy Lorentz violation, and proposed Lorentz-violating theories of quantum gravity, are ruled out by low energy tests; the only known exceptions are based on supersymmetry.
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