Nonlinear Realization of a Dynamical Poincare Symmetry by a Field-dependent Diffeomorphism

TL;DR

This paper demonstrates that certain field theories describing membranes and fluid dynamics possess a nonlinear realization of a higher-dimensional Poincare symmetry through a field-dependent diffeomorphism, revealing a hidden geometric structure.

Contribution

It introduces a novel nonlinear realization of a dynamical Poincare symmetry in membrane and fluid models via a field-dependent diffeomorphism, linking lower-dimensional theories to higher-dimensional symmetries.

Findings

The symmetry algebra matches that of a higher-dimensional Poincare group.

Membrane and fluid models exhibit a peculiar diffeomorphism symmetry involving fields.

These models provide a nonlinear representation of a dynamical Poincare group.

Abstract

We consider a description of membranes by (2,1)-dimensional field theory, or alternatively a description of irrotational, isentropic fluid motion by a field theory in any dimension. We show that these Galileo-invariant systems, as well as others related to them, admit a peculiar diffeomorphism symmetry, where the transformation rule for coordinates involves the fields. The symmetry algebra coincides with that of the Poincare group in one higher dimension. Therefore, these models provide a nonlinear representation for a dynamical Poincare group.