Causal Effective Field Theories

TL;DR

This paper investigates how low-energy causality constraints, without assumptions about high-energy physics, can restrict effective field theories, especially shift-symmetric ones, aligning with known positivity bounds from scattering amplitudes.

Contribution

It demonstrates that low-energy causality alone can produce bounds on EFTs that match those derived from scattering amplitude positivity, without relying on UV assumptions.

Findings

Low-energy causality imposes two-sided bounds on Wilson coefficients.

Bounds derived from causality agree with positivity bounds from scattering amplitudes.

Focus on shift-symmetric theories and propagation around specific backgrounds.

Abstract

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low-energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically-symmetric background. We find that low-energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from $2 \rightarrow 2$ scattering amplitude dispersion relations using full crossing symmetry.