Euler fluid in 2+1 dimensions as a gauge theory, and an action for the Euler fluid in any dimension

TL;DR

This paper develops a gauge theory framework for the Euler fluid in 2+1 dimensions, extends it to include electromagnetic coupling, and proposes an action applicable in any dimension, offering new insights into fluid topology and quantization.

Contribution

It introduces a gauge theory formulation for Euler fluids in 2+1 dimensions and extends it to any dimension with a new action, linking fluid dynamics to topological and quantum properties.

Findings

Gauge theory for 2+1D Euler fluid constructed

Extension to Euler fluid coupled with electromagnetic background

Proposed a universal action for Euler fluid in any dimension

Abstract

In this paper we parallel the construction of Tong of a gauge theory for shallow water, by writing a gauge theory for the Euler fluid in 2+1 dimensions. We then extend it to an Euler fluid coupled to electromagnetic background. We argue that the gauge theory formulation provides a topological argument for the quantization of 2+1 dimensional Euler Hopfion solution. In the process, we find a (non-gauge) action for the Euler fluid that can be extended to any dimension, including the physical 3+1 dimensions. We discuss several aspects of the ABC flow.