The unifying superalgebra OSp(1|32)

TL;DR

This paper demonstrates how the superalgebra OSp(1|32) unifies various string theories and M-theory by relating their symmetry operators, with dualities interpreted as generator redefinitions within the algebra.

Contribution

It shows that OSp(1|32) provides a single framework encompassing multiple string theories, M-theory, and F-theory through different generator identifications and duality transformations.

Findings

Unified description of string theories and M-theory via OSp(1|32)

Dualities as generator redefinitions within the algebra

Identification of different theories by translation generator choices

Abstract

We show how OSp(1|32) gives a unifying framework to describe d=10 type II string theories, d=11 M-theory and d=12 F-theory. The theories are related by different identifications of their symmetry operators as generators of OSp(1|32). T- and S-dualities are recognized as redefinitions of generators. Some (s,t) signatures of spacetime allow reality conditions on the generators. All those that allow a real structure are related again by redefinitions within the algebra, due to the fact that the algebra OSp(1|32) has only one real realization. The redefinitions include space/space, time/time and space/time dualities. A further distinction between the theories is made by the identification of the translation generator. This distinguishes various versions of type II string theories, in particular the so-called *-theories, characterized by the fact that the P_0 generator is not the (unique) positive-definite energy operator in the algebra.