Triality of Majorana-Weyl Spacetimes With Different Signatures

Details Triality of Majorana-Weyl Spacetimes With Different Signatures Triality of Majorana-Weyl Spacetimes With Different Signatures

1999-07-17

arxiv.org/abs/hep-th/9907148v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTex file

Scientific paper

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.

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