Volume Preserving Diffeomorphism and Noncommutative Branes

TL;DR

This paper explores a novel representation of volume-preserving diffeomorphisms using noncommutative branes, providing insights into their quantization and potential applications in theoretical physics.

Contribution

It introduces a new way to represent volume-preserving diffeomorphisms via noncommutative (p-2)-branes with a Hopf term, facilitating their quantization.

Findings

Representation of volume-preserving diffeomorphisms using noncommutative branes

Static gauge simplifies brane description to free fields

Quantization of the algebra appears feasible

Abstract

We give a representation of the volume preserving diffeomorphism of $\bR^p$ in terms of the noncommutative (p-2)-branes whose kinetic term is described by the Hopf term. In the static gauge, the (p-2)-brane can be described by the free fields and it suggests that the quantization of the algebra is possible.