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We focus on the question of how relativistic fluid dynamics should be thoughtof as a Wilsonian effective field theory emerging from Schwinger-Keldysh pathintegrals. Taking the basic principles of Schwinger-Keldysh formalismseriously, we are led to a series of remarkable statements and conjectures,which we phrase in terms of a broad programme relating relativistic fluiddynamics and topological sigma models. Apart from the intrinsic interest forthese ideas from the non-equilibrium field theory viewpoint, we also emphasizeits relevance to various fundamental questions in black hole physics.

The Fluid Manifesto: Emergent symmetries, hydrodynamics, and black holes