Physics NotePublished
Triality of Majorana-Weyl Spacetimes with Different Signatures
M. A. Andrade; M. Rojas; F. Toppan
1999
Publication details
- Authors
- M. A. Andrade; M. Rojas; F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 1999
- Description
- 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 <math>(1+9)\leftrightarrow (5+5)\leftrightarrow (9+1)\,\!</math> spacetimes, as well as their transverse coordinates spacetimes <math>(0+8)\leftrightarrow (4+4)\leftrightarrow (8+0)\,\!</math>. Larger dimensional spacetimes such as <math>(2+10)\leftrightarrow (6+6)\leftrightarrow (10+2)\,\!</math> 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 <math>N=1\,\!</math> superstring and superYang-Mills theories. Their dualities close the six-element permutation group <math>S_3\,\!</math> . Bilinear and trilinear invariants allowing to formulate theories with a manifest space-time symmetry are constructed.
- Year
- 1999
- Number
- CBPF-NF-O39/99
- Linked to a thesis
- No
- Linked to a grant
- No