--- title: "Triality of Majorana-Weyl Spacetimes with Different Signatures • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb45f" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Triality%2Bof%2BMajorana-Weyl%2BSpacetimes%2Bwith%2BDifferent%2BSignatures%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TS4gQS4gQW5kcmFkZTsgTS4gUm9qYXM7IEYuIFRvcHBhbg%2Cdetalhe_1999%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI0NWYi%2Cs_ynulqmWv-o6Xbfla.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Triality of Majorana-Weyl Spacetimes with Different Signatures • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Triality%2Bof%2BMajorana-Weyl%2BSpacetimes%2Bwith%2BDifferent%2BSignatures%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TS4gQS4gQW5kcmFkZTsgTS4gUm9qYXM7IEYuIFRvcHBhbg%2Cdetalhe_1999%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmI0NWYi%2Cs_ynulqmWv-o6Xbfla.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Triality of Majorana-Weyl Spacetimes with Different Signatures** **M. A. Andrade; M. Rojas; F. Toppan** 1999 [**Download PDF **0.1 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb45f/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Triality%20of%20Majorana-Weyl%20Spacetimes%20with%20Different%20Signatures) ## **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
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