Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons

TL;DR

The paper tests forward-limit analyticity/positivity constraints as a diagnostic for UV completions of Galileon-inspired theories. It analyzes a pseudo-linear massive gravity model and a generalized Proca theory, finding no positivity window for the former while showing that higher-derivative terms can restore positivity for the latter. These results imply that simple IR completions without Einstein-Hilbert interactions are unlikely to admit ordinary local UV completions, highlighting the potential necessity of gravity-like terms for a consistent high-energy completion. The forward-limit positivity constraint is powerful but not solely sufficient to determine UV viability, leaving room for nonlocal or exotic UV structures.

Abstract

We derive analyticity constraints on a nonlinear ghost-free effective theory of a massive spin-2 particle known as pseudo-linear massive gravity, and on a generalized theory of a massive spin-1 particle, both of which provide simple IR completions of Galileon theories. For pseudo-linear massive gravity we find that, unlike dRGT massive gravity, there is no window of parameter space which satisfies the analyticity constraints. For massive vectors which reduce to Galileons in the decoupling limit, we find that no two-derivative actions are compatible with positivity, but that higher derivative actions can be made compatible.