I will discuss the phenomenon of emergent Lorentz invariance in strongly coupled theories, using the gauge/gravity correspondence to handle strong dynamics. The renormalization group flow towards Lorentz invariance is imprinted in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are power-law suppressed by the ratio of the infrared and ultraviolet scales. I will comment on the implications for particle physics and condensed matter.

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