The Story of \cal O: Positivity constraints in effective field theories

TL;DR

This paper introduces a straightforward approach to determine which operators in effective field theories must have positive coefficients due to causality constraints, clarifies existing positivity arguments, and explores implications for various theories.

Contribution

It presents a new simple method for identifying causality-imposed positivity constraints and clarifies the connection between superluminal perturbations and instabilities in effective theories.

Findings

Operators with positive coefficients are linked to causality.

Superluminal perturbations relate to instabilities near the cutoff.

Implications for ghost condensate and Lorentz-violating theories.

Abstract

We propose a simple method for identifying operators in effective field theories whose coefficients must be positive by causality. We also attempt to clarify the relationship between diverse positivity arguments that have appeared in the literature. We conjecture that the superluminal perturbations identified in non-positive effective theories are generally connected to instabilities that develop near the cutoff scale. We discuss implications for the ghost condensate, the chiral Lagrangian, and the Goldstone bosons of theories with spontaneous Lorentz violation.