Tunneling into Extra Dimension and High-Energy Violation of Lorentz Invariance

TL;DR

This work explores a brane-world with infinite extra dimensions where the bulk metric breaks $SO(1,3)$, yet low-energy physics exhibits approximate Lorentz invariance. All four-dimensional fields are quasilocalized resonances rather than true bound states, possessing finite, energy-dependent widths and, for many modes, a decay probability into the bulk that grows with energy. By analyzing fermions and bosons in an asymmetrically warped background, the author derives dispersion relations and decay widths, identifies conditions under which bosons and gravitons share a reduced maximal speed, and shows that matching fermion speeds requires fine-tuning. Phenomenological constraints from cosmic rays, gamma-ray observations, and proton stability imply strong bounds on the number of extra dimensions and highlight the tension with high-dimensional embeddings, while offering a holographic interpretation in terms of couplings to a conformal sector.

Abstract

We consider a class of models with infinite extra dimension, where bulk space does not possess SO(1,3) invariance, but Lorentz invariance emerges as an approximate symmetry of the low-energy effective theory. In these models, the maximum attainable speeds of the graviton, gauge bosons and scalar particles are automatically equal to each other and smaller than the maximum speed in the bulk. Additional fine-tuning is needed in order to assure that the maximum attainable speed of fermions takes the same value. A peculiar feature of our scenario is that there are no truly localized modes. All four-dimensional particles are resonances with finite widths. The latter depends on the energy of the particle and is naturally small at low energies.