Superluminal Travel Made Possible (in two dimensions)

TL;DR

This paper demonstrates that superluminal signal propagation can occur in two-dimensional Poincare invariant quantum field theories if spatial parity is broken, leading to an unconventional causal structure with potential implications for string theory.

Contribution

It introduces a consistent two-dimensional quantum field theory with instantaneous causal structure and explores its properties and potential applications in string theory.

Findings

Superluminal signals possible in 2D quantum field theories with broken parity.

The non-linear SO(1,1) sigma-model is asymptotically free and well-defined non-perturbatively.

The model can be coupled to gravity, affecting string theory constructions.

Abstract

We argue that superluminal signal propagation is possible in consistent Poincare invariant quantum field theories in two space-time dimensions, provided spatial parity is broken. This happens due to existence of the ``instantaneous'' causal structure, with one of the light cone variables being a global time. In two dimensions this causal structure is invariant under the Poincare group if one gives up the spatial parity. As a non-trivial example of a consistent interacting quantum field theory with this causal structure we discuss a non-linear SO(1,1) sigma-model, where SO(1,1) is the Lorentz symmetry. We show that this theory is asymptotically free and argue that this model is also well defined non-perturbatively, at least for some values of parameters. It provides an example of a microscopic Poincare invariant quantum field theory with local action, but non-local physical properties. Being coupled to gravity this ``instantaneous'' theory mixes with the Liouville field. If proves to be consistent, the resulting model can be used to construct (non-critical) string theories with very unconventional properties by introducing the instantaneous causal structure on the world-sheet.