Energy's and amplitudes' positivity

TL;DR

The paper investigates how NEC, stability, and subluminality interrelate in an effective field theory with higher-derivative galileon-like interactions. By employing a conformally invariant galileon, the authors construct a stable, isotropic NEC-violating background with exactly luminal fluctuations, enabled by a highly symmetric de Sitter–like solution and a careful treatment of boundary terms. However, they show that generic weak-field backgrounds induce superluminal propagation unless the EFT cutoff is bounded by the local background value of the field, implying the NEC-violating solution cannot arise within a standard relativistic UV completion. They analyze S-matrix positivity, including forward and non-forward amplitudes, and derive constraints on the coefficients to maintain positivity while acknowledging the tension between NEC violation and Lorentz-invariant UV completions. Overall, the work reveals a nuanced connection between NEC and subluminality in EFTs and outlines the stringent conditions under which NEC-violating but stable configurations can exist without contradicting fundamental causality.

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.