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Emergent structures in open EFTs

Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we examine open extensions of three well-studied theories: the superfluid, Maxwell theory, and Einstein gravity. In gauge and gravitational theories, open terms that break advanced symmetries while preserving physical ones are not automatically consistent; they are allowed only if they lead to deformed identities among the equations of motion. We explicitly construct such a term in open gravity and show that it leads to a consistent deformation of the diffeomorphism identities.