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arXiv · 2411.03661

The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces

Grigorios Giotopoulos·Hisham Sati·Urs Schreiber
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Abstract

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 $n = 11$.

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Grigorios Giotopoulos, Hisham Sati, Urs Schreiber. 2024-11-06. The M-algebra completes the hierarchy of Super-Exceptional Tangent Spaces. https://doi.org/10.1016/j.physletb.2024.139199

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