Abstract
The requirement of diffeomorphism symmetry for the target space can lead to anomalous commutators for the energy-momentum tensor for sigma models and for fluid dynamics, if certain topological terms are added to the action. We analyze several examples . A particular topological term is shown to lead to the known effective hydrodynamics of a dense collection of vortices, i.e. the vortex fluid theory in 2+1 dimensions. The possibility of a similar vortex fluid in 3+1 dimensions, as well as a fluid of knots and links, with possible extended diffeomorphism algebras is also discussed.
Highlights
The components of the energy-momentum tensor in fluid dynamics or in a field theory will obey commutation rules which express the fact that they are the generators of diffeomorphisms
We considered some topological terms which can be added to the standard actions for sigma models and for fluid dynamics
The example of the sigma model with CP2 as the target space shows how the additional term can lead to a conflict between diffeomorphisms for the target and base spaces
Summary
The components of the energy-momentum tensor in fluid dynamics or in a field theory will obey commutation rules which express the fact that they are the generators of diffeomorphisms. It is possible that there are certain types of topological terms which can be included in the action and which can create an incompatibility between diffeomorphisms in spacetime M and on the target space M This feature can be manifest as anomalous commutation rules for the energymomentum tensor. Studies of the behavior of a quantum Hall droplet as an incompressible fluid with the possibility of nondissipative viscosity in 2 þ 1 dimensions [4] and the holographic fluid-gravity correspondence in the AdS/CFT framework [5] have been two major tracks for ongoing research Added to this is the fact that a formalism for non-Abelian fluid dynamics incorporating anomalous symmetries [6] is clearly the natural framework for interesting physical phenomena such as the chiral magnetic effect and its variants [7].
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