Energy's and amplitudes' positivity

TL;DR

This paper presents a conformally invariant galileon model that allows for stable null energy condition violations with luminal excitations, challenging the usual link between NEC, stability, and sub-luminality.

Contribution

It introduces a specific effective field theory where NEC violation does not necessarily imply superluminal propagation, providing new insights into energy conditions in QFT.

Findings

The low-energy S-matrix satisfies standard positivity constraints.

Stable NEC-violating solutions with luminal excitations are possible.

Superluminal propagation can occur in solutions outside the NEC-violating configuration.

Abstract

In QFT, the null energy condition (NEC) for a classical field configuration is usually associated with that configuration's stability against small perturbations, and with the sub-luminality of these. Here, we exhibit an effective field theory that allows for stable NEC-violating solutions with exactly luminal excitations only. The model is the recently introduced `galileon', or more precisely its conformally invariant version. We show that the theory's low-energy S-matrix obeys standard positivity as implied by dispersion relations. However we also show that if the relevant NEC-violating solution is inside the effective theory, then other (generic) solutions allow for superluminal signal propagation. While the usual association between sub-luminality and positivity is not obeyed by our example, that between NEC and sub-luminality is, albeit in a less direct way than usual.