Positivity Constraints on Lorentz-breaking EFTs

The coefficients of the operators of an effective field theory (EFT) are constrained to satisfy certain inequalities, under the (mild) assumption that the UV completion satisfies general requirements of causality and unitarity. We begin the extension of these ideas to theories where the Lorentz symmetry is spontaneously broken, as it happens in cosmology and condensed matter physics. Constraints are derived using dispersive arguments for the 2-point function of conserved currents and of the stress-energy tensor.