Non-relativistic conformal symmetries in fluid mechanics

Abstract

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schroedinger group, which also involves, in addition, Schroedinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally-invariant relativistic theory, the recently discussed Conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

Substantially revised and extended version. A new Section is added on deriving the non-relativistic fluid mechanics from relativistic conformal field theory. The breaking of Conformal Galilei symmetry (obtained by contraction) is explained by the subtle behavior of the non-relativistic limit. 18 pages no figures. Some more references added

References in corpus (11)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Galilean Conformal Algebras and AdS/CFT
• Non-relativistic conformal symmetries and Newton-Cartan structures
• The geometry of Schrödinger symmetry in non-relativistic CFT
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• On the spectrum of nonrelativistic AdS/CFT
• Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
• Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
• Remark on quantum mechanics with conformal Galilean symmetry
• CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity

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