Two-twistor Description of Membrane

TL;DR

This paper develops a twistorial formulation of D=4 membranes, expressing their dynamics through twistor fields and geometric forms, and discusses extensions to higher dimensions and supersymmetric models.

Contribution

It introduces a novel twistorial membrane model in D=4 using two twistor fields and geometric three-forms, extending twistorial descriptions to membrane theories.

Findings

Membrane momenta expressed via spinorial fields.

Purely twistorial membrane action derived from geometric three-form.

Discussion of higher-dimensional and supermembrane extensions.

Abstract

We describe D=4 twistorial membrane in terms of two twistorial three-dimensional world volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: the one with $p+1$ vectorial fourmomenta, and the second with tensorial momenta of $(p+1)$-th rank. Further we consider tensionful membrane case in D=4. By using the membrane generalization of Cartan-Penrose formula we express the fourmomenta by spinorial fields and obtain the intermediate spinor-space-time formulation. Further by expressing the worldvolume dreibein and the membrane space-time coordinate fields in terms of two twistor fields one obtains the purely twistorial formulation. It appears that the action is generated by a geometric three-form on two-twistor space. Finally we comment on higher-dimensional (D>4) twistorial p-brane models and their superextensions.