Triality of Majorana-Weyl Spacetimes With Different Signatures
Abstract
Majorana-Weyl spacetimes offer a rich algebraic setup and new types of space-time dualities besides those discussed by Hull. The triality automorphisms of Spin(8) act non-trivially on Majorana-Weyl representations and Majorana-Weyl spacetimes with different signatures. In particular relations exist among the (1+9)-(5+5)-(9+1) spacetimes, as well as their transverse coordinates spacetimes (0+8)-(4+4)-(8+0). Larger dimensional spacetimes such as (2+10)-(6+6)-(10+2) also show dualities induced by triality. A precise three-languages dictionary is here given. It furnishes the exact translations among, e.g., the three different versions (one in each signature) of the ten-dimensional N=1 superstring and superYang-Mills theories. Their dualities close the six-element permutation group S_3. Bilinear and trilinear invariants allowing to formulate theories with a manifest space-time symmetry are constructed.
Cite
@article{arxiv.hep-th/9907148,
title = {Triality of Majorana-Weyl Spacetimes With Different Signatures},
author = {M. A. De Andrade and M. Rojas and F. Toppan},
journal= {arXiv preprint arXiv:hep-th/9907148},
year = {2007}
}
Comments
11 pages, LaTex file