Fortunately, we do not live in a SUSY world, so it may be that upon SUSY breaking appropriate sized operators at each mass dimension are generated. This question has recently been explored in [65]. For CPT violating dimension five SUSY operators in SQED, the authors find that SUSY breaking yields dimension three operators of the form , where is the SUSY breaking scale, is the scale of Lorentz violation, and is an coefficient. For as light as it could be (around ), spin polarized torsion balances (see Section 5.4) are able to place limits on between . It therefore is probable that these operators are observationally unacceptable. However, dimension five SUSY operators are CPT violating, so a combination of CPT invariance and SUSY would forbid Lorentz violating operators below dimension six. The low energy dimension four operators induced by SUSY breaking in the presence of dimension six operators would then presumably be suppressed by . This is enough suppression to be compatible with current experiment if is at the Planck scale and .

Another method by which Lorentz violation can occur but might have small dimension matter operators is via extra dimension scenarios. For example, in [70] a braneworld scenario was considered where four-dimensional Lorentz invariance was preserved on the brane but broken in the bulk. The only particle which can then directly see Lorentz violation is the graviton - the matter fields, being trapped on the brane, can only feel the bulk Lorentz violation through graviton loops. The induced dimension operators can be quite small, depending on the exact extra-dimension scenario considered. Note though that this approach has been criticized in [91], whose authors argue that significant Lorentz violation in the infrared would still occur.

In summary, the current status of Lorentz violation in EFT is mildly disconcerting for a phenomenologist (if one really wants to believe in Lorentz violation). From an EFT point of view, without custodial symmetries one would expect that we would have seen signs of Lorentz violation by now. Imposing SUSY + CPT or a braneworld scenario may fix this problem, but then we are left with a model with more theoretical assumptions. Furthermore a SUSY + CPT model is unlikely to ever be testable with astrophysics experiments and requires significant improvement in terrestrial experiments to be seen [65]. Fortunately, since this is a phenomenological review we can blithely ignore the above considerations and simply classify and constrain all possible operators at each mass dimension. This is also the safest approach. After all, we are searching for a possible signal from the mysterious realm of quantum gravity and so must be careful about overly restricting our models.

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