Effective Field Theories (EFTs) appear everywhere there is a mass scale. They serve to simplify complex multiscale problems, and as general tools to parametrise the unknown or incalculable (e.g. the pion chiral Lagrangian, gravity, or physics beyond the standard model - BSM). I will present how dispersion relations single out EFTs that originate from microscopic unitary theories, both at weak and at strong coupling. This reshapes the landscape of plausible physics BSM, and I will show that massive gravity, theories with isolated massive higher-spin particles, and theories with very irrelevant interactions, don’t posses healthy UV completions.
