Within the most general linear axions Einstein Maxwell dilation model(EMD), translational and rotational symmetry are both broken. Recovering translation invariance is not as much as simple to restore the rotational one. For the latter it is enough to set the condition Yx(φ)kx2=Yy(φ)ky2 while for the former it is not so straightforward.
Maxwell's electromagnetic equations exhibit cylindrical symmetry. See, Article Pythagoras's Theorem in Seven Dimensions
As regards matters relating to translational motion, you should check out the Newton's Cradle. See, Article Newton's Cradle Disproves Einstein's Theories of Relativity
- Holography without translational symmetry, David Vegh, https://arxiv.org/pdf/1301.0537.pdf
- Scale-invariant hyperscaling-violating holographic theories and the resistivity of strange metals with random-field disorder, Andrew Lucas, Subir Sachdev, Koenraad Schalm, https://arxiv.org/pdf/1401.7993.pdf
- Holographic Phonons, Lasma Alberte, Martin Ammon, Amadeo Jiménez-Alba, Matteo Baggioli, Oriol Pujolàs, Phys.Rev.Lett. 120 (2018), https://arxiv.org/pdf/1711.03100.pdf
Also see this Ph.D thesis, from Universidad Aut ́onoma de Madrid, by Amadeo Jim ́enez, which discusses various ways of symmetry breaking in Holographic models, spontaneous breaking, anomalous breaking, transport phenomenon and so on, http://inspirehep.net/record/1607633/files/fulltext.pdf
Hi Gian Andrea,
You can write an email to me and Amadeo.
We both worked and are working on those topics...
Ciao
Matteo
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