Are 1+1 and 2+2 exceptional signatures?

TL;DR

This paper demonstrates that the signatures 1+1 and 2+2 are unique in certain spacetime models of 0-branes, linking their exceptional nature to underlying symmetries and mathematical structures.

Contribution

It provides a proof that 1+1 and 2+2 signatures are exceptional, based on symmetry considerations, and explores their relation via the concept of a 'quatl' 0-brane.

Findings

1+1 and 2+2 signatures are proven to be exceptional.

The signatures are related through the 'quatl' 0-brane model.

2+2 spacetime can be viewed as a worldvolume or matrix-brane.

Abstract

We prove that 1+1 and 2+2 target `spacetimes' of a 0-brane are exceptional signatures. Our proof is based on the requirement of SL(2,R) and `Lorentz' symmetries of a first order lagrangian. Using a special kind of 0-brane called `quatl', we also show that the exceptional signatures 1+1 and 2+2 are closely related. Moreover, we argue that the 2+2 target `spacetime' can be understood either as 2+2 worldvolume `spacetime' or as `1+1-matrix-brane'. The possibility that the exceptional 2+2-signature implies an exceptional chirotope is briefly outlined.