"Planck-scale physics" of vacuum in a strong magnetic field

TL;DR

This paper explores how vacuum in a strong magnetic field behaves like a hyperbolic metamaterial, providing an analogy for Planck-scale physics and Lorentz symmetry violation at small scales.

Contribution

It demonstrates that vacuum under strong magnetic fields exhibits hyperbolic metamaterial properties, offering a new analogy for Planck-scale physics and Lorentz symmetry breaking.

Findings

Vacuum in strong magnetic fields acts as a hyperbolic metamaterial.

An effective Lorentz symmetry-violating 'Planck scale' can be defined.

Presence of a 'heavy' extraordinary photon with ~2 GeV mass.

Abstract

It is widely believed that Lorentz symmetry of physical vacuum is broken near the Planck scale. Here we show that recently demonstrated "hyperbolic metamaterial" behaviour of vacuum in a strong magnetic field provides us with an interesting analogy of the Planck-scale physics. As demonstrated by Chernodub, strong magnetic field forces vacuum to develop real condensates of electrically charged \rho mesons, which form an anisotropic inhomogeneous superconducting state similar to Abrikosov vortex lattice. As far as electromagnetic field behaviour is concerned, this hyperbolic metamaterial state of vacuum exhibits effective 3D Lorentz symmetry, which is broken at small scale (large momenta) due to spatial dispersion. Thus, an effective Lorentz symmetry-violating "Planck scale" may be introduced. Near the critical magnetic field this effective "Planck scale" is much larger than the metamaterial periodicity defined by the \rho meson lattice. Similar to regular hyperbolic metamaterials, spatial dispersion of vacuum in a strong magnetic field leads to appearance of the "additional wave", which manifests itself as a "heavy" extraordinary photon with an effective mass ~2GeV.