The Signature Triality of Majorana-Weyl Spacetimes

TL;DR

This paper explores the triality automorphisms in higher-dimensional Majorana-Weyl spacetimes, revealing how various theories like superstrings and branes are interconnected through space-time dualities and automorphisms.

Contribution

It introduces bilinear and trilinear invariants under space-time triality and analyzes Cartan's vector and spinor triality in detail with explicit formulas.

Findings

Interconnection of theories via S_3 permutation group

Introduction of invariants under space-time triality

Explicit formulas for Cartan's triality in Majorana-Weyl basis

Abstract

Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's, superstrings, five-branes, F-theory, are shown to be interconnected via the S_3 permutation group. Bilinear and trilinear invariants under space-time triality are introduced and their possible relevance in building models possessing a space-versus-time exchange symmetry is discussed. Moreover the Cartan's ``vector/chiral spinor/antichiral spinor" triality of SO(8) and SO(4,4) is analyzed in detail and explicit formulas are produced in a Majorana-Weyl basis. This paper is the extended version of hep-th/9907148.