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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.07576 |
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| author | Julia, Bernard L. |
| author_facet | Julia, Bernard L. |
| contents | We present the historical path from General relativity to the construction of Maximal $\mathcal{N}_4 = 8$ Supergravity with a detour in D=10 and 11 dimensions. The supergravities obtained by toric dimensional reduction and/or by reducing the number of supersymmetry generators have large exceptional duality symmetry groups and exhibit a remarkably uniform pattern across all values of $\mathcal{N}_D$ and D. In particular (bosonic) General relativity fits in as the simplest case and anchors us to the Real world. Dimensional reduction to 2 dimensions brings us to affine Kac-Moody groups and their semi-direct products with a real form of the Witt algebra: there is "integrable Magics". Integrability of 4D Gravity and of its reduction to 2D is considered with their "Twisted self-duality". Hyperbolic Kac-Moody symmetries appear after reduction to 1D: this leads to "chaotic Magics". We then discover "Borcherds"-Kac-Moody symmetries that allow us to rewrite in any dimension all matter equations of motion as Twisted self-duality: "Algebraic geometric Magics". Finally a "BF" metasymmetry $Σ$ exchanges negative quartets of Fermionic dimensions with Bosonic ones inside two Magic triangles. A third ubiquitous triangle of symmetries from Invariant theory resists unification despite its strong resemblance to the others. The prospective remarks include seven Challenges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07576 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An exceptional story: Symmetries and dualities between Maximal supergravity and General relativity Julia, Bernard L. High Energy Physics - Theory We present the historical path from General relativity to the construction of Maximal $\mathcal{N}_4 = 8$ Supergravity with a detour in D=10 and 11 dimensions. The supergravities obtained by toric dimensional reduction and/or by reducing the number of supersymmetry generators have large exceptional duality symmetry groups and exhibit a remarkably uniform pattern across all values of $\mathcal{N}_D$ and D. In particular (bosonic) General relativity fits in as the simplest case and anchors us to the Real world. Dimensional reduction to 2 dimensions brings us to affine Kac-Moody groups and their semi-direct products with a real form of the Witt algebra: there is "integrable Magics". Integrability of 4D Gravity and of its reduction to 2D is considered with their "Twisted self-duality". Hyperbolic Kac-Moody symmetries appear after reduction to 1D: this leads to "chaotic Magics". We then discover "Borcherds"-Kac-Moody symmetries that allow us to rewrite in any dimension all matter equations of motion as Twisted self-duality: "Algebraic geometric Magics". Finally a "BF" metasymmetry $Σ$ exchanges negative quartets of Fermionic dimensions with Bosonic ones inside two Magic triangles. A third ubiquitous triangle of symmetries from Invariant theory resists unification despite its strong resemblance to the others. The prospective remarks include seven Challenges. |
| title | An exceptional story: Symmetries and dualities between Maximal supergravity and General relativity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.07576 |