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Effective Field Theories (EFTs)—or Quantum Field Theories applicable at long distances or low energies—play a crucial role across various areas of physics, including particle physics, cosmology, and condensed matter systems. Consequently, constraining the landscape of consistent EFTs is both a significant and valuable endeavor. In this talk, I will explore how the Lorentz-invariant principle of causality leads to nontrivial "positivity" constraints on low-energy EFTs. Specifically, I will compare two distinct approaches for deriving these constraints: the "IR incarnation," which requires that fluctuations around any nontrivial background propagate subluminally, and the "UV incarnation," which relies on dispersion relations for forward-limit 2→2 scattering amplitudes. I will also highlight the complications introduced by loop effects and discuss recent progress toward addressing these challenges. |