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

Positivity bounds on effective field theories with spontaneously broken Lorentz invariance