(p+1)-Algebra for Super p-Brane: the Nambu Bracket Reformulation

TL;DR

This paper reformulates super p-brane actions and equations of motion using Nambu (p+1)-brackets, revealing their (p+1)-algebra structure in both flat and curved superspaces.

Contribution

It introduces a Nambu bracket-based reformulation of super p-brane actions, making their algebraic structure explicit and providing a new mathematical framework.

Findings

Manifest (p+1)-algebra structure in super p-branes

Reformulation in terms of differential forms for flat superspace

Applicable to both flat and curved superspaces

Abstract

We express the covariant actions of a super p-brane and the corresponding equations of motion, in the flat and curved superspaces, in terms of the Nambu (p+1)-brackets. These brackets make the (p+1)-algebra structure of super p-brane manifest. For the flat superspace, this reconstruction of the action also allows reformulating it in terms of two sets of differential forms.