The twelve dimensional super (2+2)-brane

TL;DR

This paper develops a covariant supersymmetric action for a super (2+2)-brane in twelve dimensions, demonstrating its relation to M-theory and type IIB string theory through superspace compactification.

Contribution

It introduces a novel twelve-dimensional superspace framework and constructs a super (2+2)-brane action, linking it to M-theory and type IIB string theory.

Findings

Constructed a trivial superspace in 12D with (2,2) signature.

Derived membrane and string actions via superspace compactification.

Unified the algebraic structures of M-theory and type IIB string theory in 12D.

Abstract

We discuss supersymmetry in twelve dimensions and present a covariant supersymmetric action for a brane with worldsheet signature (2,2), called a super (2+2)-brane, propagating in the osp(64,12) superspace. This superspace is explicitly constructed, and is trivial in the sense that the spinorial part is a trivial bundle over spacetime, unlike the twisted superspace of usual Poincare supersymmetry. For consistency, it is necessary to take a projection of the superspace. This is the same as the projection required for worldvolume supersymmetry. Upon compactification of this superspace, a torsion is naturally introduced and we produce the membrane and type IIB string actions in 11 and 10 dimensional Minkowski spacetimes. In addition, the compactification of the twelve dimensional supersymmetry algebra produces the correct algebras for these theories, including central charges. These considerations thus give the type IIB string and M-theory a single twelve dimensional origin.