Positivity-causality competition: a road to ultimate EFT consistency constraints

TL;DR

This paper explores how unitarity, causality, and positivity bounds jointly constrain the parameters of photon effective field theories, providing a comprehensive approach to ensure their consistency.

Contribution

It analytically derives unitarity and causality constraints on photon EFTs and compares their effectiveness in bounding Wilson coefficients.

Findings

Causality constraints complement positivity bounds.

Combined constraints significantly narrow EFT parameter space.

Analytic derivation of bounds enhances understanding of EFT consistency.

Abstract

Effective field theories (EFT) are strongly constrained by fundamental principles such as unitarity, locality, causality, and Lorentz invariance. In this paper, we consider the EFT of photons (or other $U(1)$ gauge field) and compare different approaches to obtain bounds on its Wilson coefficients. We present an analytic derivation of the implications of unitarity (linear and non-linear positivity bounds) and compare these constraints with the requirement of causal propagation of the photon modes around non-trivial backgrounds generated by external sources. We find that the low energy causality condition can give complementary constraints to the positivity bounds. Applying both constraints together can significantly reduce the allowed region of the photon EFT parameters.