Topological Terms and Diffeomorphism Anomalies in Fluid Dynamics and Sigma Models

TL;DR

This paper explores how topological terms induce diffeomorphism anomalies in fluid dynamics and sigma models, leading to vortex and knot fluid theories with potential extended symmetries.

Contribution

It demonstrates the role of topological terms in generating anomalies and connects them to effective vortex and knot fluid models in various dimensions.

Findings

Topological terms cause anomalous energy-momentum commutators.

Vortex fluid theory in 2+1 dimensions is derived from topological actions.

Discussion of possible vortex and knot fluids in 3+1 dimensions.

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.