Lorentz violation, Gravity, Dissipation and Holography

We reconsider Lorentz Violation (LV) at the fundamental level. We show that Lorentz Violation is intimately connected with gravity and that LV couplings in QFT must always be fields in a gravitational sector. Diffeomorphism invariance must be intact and the LV couplings transform as tensors under coordinate/frame changes. Therefore searching for LV is one of the most sensitive ways of looking for new physics, either new interactions or modifications of known ones. Energy dissipation/Cerenkov radiation is shown to be a generic feature of LV in QFT. A general computation is done in strongly coupled theories with gravity duals. It is shown that in scale invariant regimes, the energy dissipation rate depends non-triviallly on two characteristic exponents, the Lifshitz exponent and the hyperscaling violation exponent.

💡 Research Summary

The paper revisits the notion of Lorentz Violation (LV) at a fundamental level and demonstrates that LV cannot be treated as a mere external background in quantum field theory (QFT); instead, it must be embedded within the gravitational sector as dynamical fields. By insisting on the preservation of diffeomorphism invariance, the authors argue that LV couplings must transform as tensors under general coordinate transformations. This requirement forces any LV parameter to be a component of a gravitational field (e.g., a vector or tensor field) rather than a fixed scalar, ensuring that the full theory remains generally covariant. Consequently, experimental searches for LV become exceptionally sensitive probes of new physics, because any detected deviation would imply either a novel interaction in the gravitational sector or a modification of the known gravitational dynamics.

The second major theme of the paper is the generic occurrence of energy dissipation—most familiarly manifested as Cherenkov radiation—whenever LV is present. In a Lorentz‑violating medium, particles can travel faster than the local phase velocity of light, leading to spontaneous emission of radiation and a corresponding loss of kinetic energy. While this effect is well understood in weakly coupled, perturbative QFT, the authors point out that in strongly coupled systems the standard perturbative tools break down. To overcome this, they employ the gauge/gravity (holographic) correspondence, constructing a dual gravitational background that captures the essential LV features of the boundary field theory.

The holographic model is built on a generalized Lifshitz‑type metric that incorporates two critical exponents: the dynamical (Lifshitz) exponent (z) and the hyperscaling‑violation exponent (\theta). The metric takes the form
\