Causality, Unitarity and Symmetry in Effective Field Theory

TL;DR

This paper develops a causality- and unitarity-based framework to constrain effective field theories via forward-limit dispersion relations at mass dimension eight. By recasting the UV completions as a convex cone of allowed UV couplings and using extremal rays, it derives concrete positivity bounds on elastic and inelastic amplitudes, including effects from loops of dimension-6 operators. The analysis spans complex scalar, spinning particles, internal symmetries, flavour structure, and helicity, and extends to supersymmetric EFTs where positivity theorems are unified across multiplets. The results have direct implications for SMEFT and model-building, providing systematic, geometry-backed constraints on symmetry breaking and offering tools for future exploration beyond the forward limit and into higher dimensions or massive theories.

Abstract

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension $8$ operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in $SU(2)$ and $SU(3)$ global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension $6$ operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension $8$ and $4$ legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.