A New Spinning Membrane Lagrangian

TL;DR

This paper introduces a new polynomial, local supersymmetric Lagrangian for the bosonic membrane, emphasizing the trade-offs between polynomiality, supersymmetry types, and the elimination of auxiliary fields.

Contribution

It presents a novel polynomial Lagrangian for the bosonic membrane that differs from previous models by facilitating quantization and analyzing supersymmetry constraints.

Findings

The new Lagrangian is polynomial in fields, aiding quantization.

Linearly realized supersymmetry must be limited to Q supersymmetry after auxiliary field elimination.

Full Q+S supersymmetry requires a non-polynomial action.

Abstract

A new local world volume supersymmetric Lagrangian for the bosonic membrane is presented. The starting Lagrangian is the one constructed by Dolan and Tchrakian with vanishing cosmological constant, with quadratic and quartic derivative terms. Our Lagrangian differs from the one constructed by Lindstrom and Rocek in the fact that it is polynomial in the fields facilitating the quantization process. It is argued, rigorously, that if one wishes to construct polynomial actions without a curvature scalar term and, where supersymmetry is linearly realized in the space of physical fields, after the elimination of auxiliary fields, one must relinquish $S$ supersymmetry, altogether, and concentrate solely on the $Q$ supersymmetry associated with the superconformal algebra in three dimensions. A full $''Q+S''$ supersymmetry cannot be implemented in a linearly realized way satisfying all of the above-mentioned requirements, unless a non-polynomial action is chosen. PACS:04.65.+e, 04.20.Fy.