From Scattering Amplitudes to Subluminal Propagation: Positivity in EFTs

Effective Field Theories (EFTs)—quantum field theories that
encapsulate physical phenomena at large distances or low energies—serve as
essential frameworks across a broad spectrum of theoretical physics, from
particle physics and cosmology to condensed matter theory. Gaining insight
into the principles that delineate the landscape of consistent EFTs is
thus a question of profound and far-reaching significance.

In this talk, I will delve into the deep interplay between causality, as
encoded in Lorentz invariance, and the structure of low-energy EFTs.
Specifically, I will demonstrate how causality imposes robust and highly
nontrivial positivity constraints on the effective interactions. Two
complementary methodologies for deriving these constraints will be
explored: the infrared (IR) perspective, which ensures that perturbations
around nontrivial background configurations propagate subluminally, and
the ultraviolet (UV) perspective, which leverages analytic dispersion
relations applied to forward-limit 2→2 scattering amplitudes. Along the
way, we will confront the subtleties introduced by quantum loop
corrections and highlight recent developments aimed at resolving these
intricacies.