Linear and nonlinear realizations of superbranes

TL;DR

This paper explores the connection between linear and nonlinear formulations of supermembranes, showing how coordinate transformations relate their actions and how constraints correspond to specific limits of nonlinear realizations.

Contribution

It introduces explicit coordinate transformations linking linear and nonlinear supermembrane actions and clarifies the role of the Rocek-Tseytlin constraint within this framework.

Findings

The Rocek-Tseytlin constraint is equivalent to a limit of the nonlinear realization.

Coordinate transformations can directly relate linear and nonlinear supermembrane actions.

The massive mode field vanishes in the nonlinear realization limit.

Abstract

The coordinate transformations which establish the direct relationship between the actions of linear and nonlinear realizations of supermembranes are proposed. It is shown that the Rocek-Tseytlin constraint known in the framework of the linear realization of the theory is simply equivalent to a limit of a "pure" nonlinear realization in which the field describing the massive mode of the supermembrane puts to zero.