Approaches to Quantum Gravity

Lorentz invariance violation & its role in Quantum Gravity phenomenology 539algebra, invoking the latter to protect the former is not entirely consistent [35].They then observe that they would actually need only the translation subalgebra ofthe Poincaré algebra to be unbroken. However, it is hard to envision a situation inwhich a granular space-time would have the full translation group as a full continuoussymmetry. Moreover as is well known, even if it is there at some level,supersymmetry must be broken at low energies. Then it is difficult to understandhow it could protect the low energy phenomena from the LIV we have been discussing,while allowing at the same time for violations to be observable at higherenergy scales that are closer to that energy regime where supersymmetry is presumablyunbroken. In fact in a recent work Bolokov, Nibbelink and Pospelov [14]noted that the most supersymmetry seems to do is to decrease the severity of therequired fine tuning. It seems that in the case of noncommutative field theories noteven exact supersymmetry would prevent large violations of Lorentz invariance.Liberati et al. [50] treat a condensed matter model of two component Bose–Einstein condensate as a model system. LI is associated with monometricity in thepropagation of the two types of quasi-particles. In this type of study one says thatthere is monometricity if the various independently propagating modes do so in thesame “effective metric” that results from the condensed matter background. Theauthors show that LI can, under certain conditions, be violated at high energieswhile being preserved at low energies. This is achieved by fine tuning a certainparameter in the model (the interaction with an external laser source) to ensuremonometricity in the hydrodynamical limit. The fine tuning is in agreement withour general results.The conclusion the authors reach in those studies is in agreement with wellknown expectations: that an emergent symmetry could give protection for theLorentz Invariance. In their case the monometricity appears to be protected by anemergent SO(2) symmetry, in the sense that once imposed at the hydrodynamicallevel it is only residually broken beyond that limit. For us the issues would be then:What physical mechanism is that which ensures monometricity at the hydrodynamicallevel? What is its analog in the space-time/particle-physics arena? Finally,what are the hopes that this type of mechanism would succeed in ensuring monometricityfor a very different type of propagating modes, such as gauge fields ascompared with standard fermion matter fields?As Liberati, Sonego and Visser [49] discuss in another paper, which we willsummarize in the discussion in Section 27.9, it is possible that more fundamentalissues come into play, perhaps concerned with measurement in a theory with adynamical space-time. These issues would of course make even the principles ofthe derivation of an EFT quite different than in normal QFTs. But they wouldalso remove the rationale for simple estimates for the sizes of higher dimensionLorentz-violating operators in an EFT.