Generalised supersymmetry and p-brane actions

TL;DR

This paper explores the most general N=1 supersymmetry algebra extensions, introduces new superspaces and spinors, and discusses novel p-brane types, revealing twelve dimensions as maximal and challenging traditional supersymmetry assumptions.

Contribution

It presents a comprehensive analysis of generalized supersymmetry algebras, introduces new superspaces and spinor classes, and proposes novel p-brane models with potential implications for higher-dimensional theories.

Findings

Supersymmetry algebra extensions are more general than previously thought.

Two distinct types of grading and superspaces are identified.

New p-brane types are discovered, with twelve dimensions as the maximum.

Abstract

We investigate the most general N=1 graded extension of the Poincare algebra, and find the corresponding supersymmetry transformations and the associated superspaces. We find that the supersymmetry for which {Q,Q} = P is not special, and in fact must be treated democratically with a whole class of supersymmetries. We show that there are two distinct types of grading, and a new class of general spinors is defined. The associated superspaces are shown to be either of the usual type, or flat with no torsion. p-branes are discussed in these general superspaces and twelve dimensions emerges as maximal. New types of brane are discovered which could explain many features of the standard p-brane theories.