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

TL;DR

The paper proposes that relativistic hydrodynamics can be derived as a Wilsonian effective field theory from Schwinger-Keldysh path integrals by elevating the doubled SK structure to a topological, cohomological framework with an emergent ${U(1)_{\sf T}}$ gauge invariance that encodes entropy. It identifies three core features—field doubling with a BRST-like symmetry, a topological subsector for difference operators, and KMS-related charges that become local in the hydrodynamic limit—and shows how these yield a twisted supersymmetric sigma-model description of fluids, with entropy current arising as a Noether current. Evidence is provided via Mathai-Quillen/MSR constructions, a topological interpretation of Brownian branes, and connections to dissipation and fluctuation relations; the framework further extends to black hole physics through the fluid/gravity correspondence, positing a $U(1)_{\sf T}$ brane in the bulk that encapsulates thermodynamic and entropic data and offers a holographic route to ER=EPR–like ideas. Collectively, the work lays out a coherent algebraic/topological foundation for non-equilibrium QFT, clarifying dissipation, entropy production, and their holographic incarnations while pointing to concrete structures (e.g., ${\cal N}_T=2$ equivariant cohomology) to be developed in future work.

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.