Superluminal Travel, UV/IR Mixing and Turbulence in the Lineland

TL;DR

This paper explores a two-dimensional quantum field theory with instantaneous causality, revealing UV/IR mixing, turbulence, and the possibility of creating arbitrarily heavy particles over time.

Contribution

It introduces a renormalizable Lorentz-invariant model with instantaneous causal structure and analyzes its unique UV/IR mixing and turbulence phenomena.

Findings

All excitations become arbitrarily low energy at high momenta.

Thermal equilibrium is impossible due to UV/IR mixing.

Heavy particles can be produced by waiting long enough.

Abstract

We study renormalizable Lorentz invariant stable quantum field theories in two space-time dimensions with instantaneous causal structure (causal ordering induced by the light "cone" time ordering). These models provide a candidate UV-completion of the two-dimensional ghost condensate. They exhibit a peculiar UV/IR mixing - energies of all excitations become arbitrarily small at high spatial momenta. We discuss several phenomena associated with this mixing. These include the impossibility to reach a thermal equilibrium and metastability of all excitations towards decay into short wavelength modes resulting in an indefinite turbulent cascade. In spite of the UV/IR mixing in many cases the UV physics can still be decoupled from low energy phenomena. However, a patient observer in the Lineland is able to produce arbitrarily heavy particles simply by waiting for a long enough time.