Positivity bounds without boosts: New constraints on low energy effective field theories from the UV
Tanguy Grall, Scott Melville
Abstract
We derive new positivity bounds for low-energy effective field theories (EFTs) that are not invariant under Lorentz boosts. ``Positivity bounds'' are the low-energy manifestation of certain fundamental properties in the UV---to date, they have been used to constrain a wide variety of EFTs; however, since existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. Assuming that the low-energy degrees of freedom can be extended into the UV in a way consistent with the fundamental axioms of unitarity, analyticity, and locality, we derive an infinite family of bounds that (derivatives of) the $2\ensuremath{\rightarrow}2$ EFT scattering amplitude must satisfy even when Lorentz boosts are broken. We apply these bounds to the leading-order EFT of both a superfluid and the scalar fluctuations produced during inflation, comparing in the latter case with the current observational constraints on primordial non-Gaussianity, demonstrating that these bounds open a new window into the high-energy physics that lies beneath our low-energy measurements.