Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory

TL;DR

This paper explores generalized superalgebras in various dimensions using division algebras, culminating in an octonionic M-theory with fewer bosonic generators and a novel equivalence between M2 and M5 sectors.

Contribution

It introduces an octonionic M-theory framework by extending superalgebras with octonions, reducing bosonic generators and revealing new symmetries.

Findings

Octonionic M-theory has 52 bosonic generators, fewer than standard M-theory.

Establishes an equivalence between octonionic M2 and M5 sectors.

Defines an octonionic generalized conformal M-superalgebra with 239 bosonic generators.

Abstract

We describe the set of generalized Poincare and conformal superalgebras in D=4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are described for D=4 by OSp(1;8| R), for D=5 by SU(4,4;1) and for D=7 by U_\alpha U(8;1|H). The relation with other schemes, in particular the framework of conformal spin (super)algebras and Jordan (super)algebras is discussed. By extending the division-algebra-valued superalgebras to octonions we get in D=11 an octonionic generalized Poincare superalgebra, which we call octonionic M-algebra, describing the octonionic M-theory. It contains 32 real supercharges but, due to the octonionic structure, only 52 real bosonic generators remain independent in place of the 528 bosonic charges of standard M-algebra. In octonionic M-theory there is a sort of equivalence between the octonionic M2 (supermembrane) and the octonionic M5 (super-5-brane) sectors. We also define the octonionic generalized conformal M-superalgebra, with 239 bosonic generators.