Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields

TL;DR

The paper shows that, under forward-limit positivity bounds, the leading elastic 2→2 interactions of both single and multiple interacting pseudo-linear spin-2 fields cannot be embedded in a standard local UV completion. By analyzing a comprehensive set of polarization configurations (SVT and transversity) and extending from one field to an arbitrary number of fields, the authors demonstrate that all leading self- and cross-couplings must vanish to satisfy positivity, with only higher-order $\ ext{(EFT)}$ operators potentially contributing positively in a limited window. The generalization to any number of fields strengthens the conclusion that the EFT expansion for pseudo-linear spin-2 fields must be organized with vanishing leading interactions unless nonlocal or nonstandard UV completions are allowed. These results underscore the power and limits of positivity bounds in constraining spin-2 EFTs and have implications for model-building in massive spin-2 scenarios, including connections to gravity-inspired constructions and condensed-matter analogs.

Abstract

We explore the effective field theory for single and multiple interacting pseudo-linear spin-2 fields. By applying forward limit positivity bounds, we show that among the parameters contributing to elastic tree level scattering amplitude, there is no region of compatibility of the leading interactions with a standard local UV completion. Our result generalizes to any number of interacting pseudo-linear spin-2 fields. These results have significant implications for the organization of the effective field theory expansion for pseudo-linear fields.