Positivity bounds on effective field theories with spontaneously broken Lorentz invariance

TL;DR

This paper derives positivity bounds on effective field theories with spontaneously broken Lorentz invariance, using analytic properties of Green's functions, applicable to cosmology and condensed matter, exemplified by conformal superfluids.

Contribution

It introduces a general method to establish positivity bounds in EFTs with broken boosts, assuming UV conformality, and applies it to conformal superfluids in three dimensions.

Findings

Derived inequalities for EFT coefficients at NLO and NNLO

Applicable to both cosmology and condensed matter systems

Provides a universal approach based on Green's function analyticity

Abstract

We derive positivity bounds on EFT coefficients in theories where boosts are spontaneously broken. We employ the analytic properties of the retarded Green's function of conserved currents (or of the stress-energy tensor) and assume the theory becomes conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example, we look at the EFT of conformal superfluids which describes the universal low-energy dynamics of CFT's at large chemical potential and we derive inequalities on the coefficients of the operators, in three dimensions, at NLO and NNLO.