Spacetime symmetries are at the basis of quantum field theory (QFT) and general relativity, the two pillars of modern physics. It is then natural to investigate and question the very nature of these symmetries, e.g. whether they are exact or accidental, i.e. emerging in the low-energy world that we can access with present experiments. (Local) Lorentz invariance (LI) is one of the best-tested symmetries of Nature. Presently it appears to be an exact symmetry since tests of Lorentz invariance violations (LIV) have provided stringent bounds on possible violations. See [Liberati, **Class.Quant.Grav. 30 (2013) 133001** ] for a review.

However, several quantum gravity approaches seem to entail violations (or modifications) of Lorentz symmetry at the fundamental level. It is then interesting to test if such violations can be detected or alternatively used to rule out some QG scenario. But one should realize that, apart from the observational constraints, LIV raise also theoretical concerns. Indeed, in the Effective Field Theory paradigm when LIV are present then a radiative correction can make them affect in a significant way low-energy physics and thus spoil the viability of models introducing such violations.

In [Belenchia, Gambassi, Liberati,

JHEP 1606 (2016) 049 ] we consider the percolation of LIV to low-energy. We show that in some relevant cases the percolation can be suppressed and discuss how this suppression generically scales with energy. Furthermore, we also consider the case of dissipative QFT which is usually neglected.

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