Abstract
We focus on the question of how relativistic fluid dynamics should be thought
of as a Wilsonian effective field theory emerging from Schwinger-Keldysh path
integrals. Taking the basic principles of Schwinger-Keldysh formalism
seriously, we are led to a series of remarkable statements and conjectures,
which we phrase in terms of a broad programme relating relativistic fluid
dynamics and topological sigma models. Apart from the intrinsic interest for
these ideas from the non-equilibrium field theory viewpoint, we also emphasize
its relevance to various fundamental questions in black hole physics.
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