The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915069278814208 |
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| author | Giotopoulos, Grigorios Sati, Hisham Schreiber, Urs |
| author_facet | Giotopoulos, Grigorios Sati, Hisham Schreiber, Urs |
| contents | The conjectured symmetries of M-theory famously involve (1.) brane-extended super-symmetry (the M-algebra) and (2.) exceptional duality-symmetry (the $\mathfrak{e}_{11}$-algebra); but little attention has been given to their inevitable combination.
In this little note, we highlight (by combining results available in the literature) that the $local$ exceptional duality-symmetry (the hyperbolic involutory $\mathfrak{k}_{1,10} \subset \mathfrak{e}_{11}$) acts on the M-algebra, through the "brane-rotating symmetry" $\mathfrak{sl}_{32}$, in a way which extends the known hierarchy of finite-dimensional $n$-exceptional tangent spaces compatibly beyond the traditional bound of $n \leq 7$ all the way to $n = 11$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces Giotopoulos, Grigorios Sati, Hisham Schreiber, Urs High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry The conjectured symmetries of M-theory famously involve (1.) brane-extended super-symmetry (the M-algebra) and (2.) exceptional duality-symmetry (the $\mathfrak{e}_{11}$-algebra); but little attention has been given to their inevitable combination. In this little note, we highlight (by combining results available in the literature) that the $local$ exceptional duality-symmetry (the hyperbolic involutory $\mathfrak{k}_{1,10} \subset \mathfrak{e}_{11}$) acts on the M-algebra, through the "brane-rotating symmetry" $\mathfrak{sl}_{32}$, in a way which extends the known hierarchy of finite-dimensional $n$-exceptional tangent spaces compatibly beyond the traditional bound of $n \leq 7$ all the way to $n = 11$. |
| title | The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2411.03661 |