The Hidden M-Group
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908755159941120 |
|---|---|
| author | Giotopoulos, Grigorios Sati, Hisham Schreiber, Urs |
| author_facet | Giotopoulos, Grigorios Sati, Hisham Schreiber, Urs |
| contents | Following arguments that the (hidden) M-algebra serves as the maximal super-exceptional tangent space for 11D supergravity, we make explicit here its integration to a (super-Lie) group. This is equipped with a left-invariant extension of the ''decomposed'' M-theory 3-form, such that it constitutes the Kleinian space on which super-exceptional spacetimes are to be locally modeled as Cartan geometries.
As a simple but consequential application, we highlight how to describe lattice subgroups $\mathbb{Z}^{k \leq 528}$ of the hidden M-group that allow to toroidially compactify also the ''hidden'' dimensions of a super-exceptional spacetime, akin to the familiar situation in topological T-duality.
In order to deal with subtleties in these constructions, we (i) provide a computer-checked re-derivation of the ''decompose'' M-theory 3-form, and (ii) present a streamlined conception of super-Lie groups, that is both rigorous while still close to physics intuition and practice.
Thereby this article highlights modernized super-Lie theory along the example of the hidden M-algebra, with an eye towards laying foundations for super-exceptional geometry. Among new observations is the dimensional reduction of the hidden M-algebra to a ''hidden IIA-algebra'' which in a companion article we explain as the exceptional extension of the T-duality doubled super-spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hidden M-Group Giotopoulos, Grigorios Sati, Hisham Schreiber, Urs High Energy Physics - Theory Mathematical Physics Differential Geometry Following arguments that the (hidden) M-algebra serves as the maximal super-exceptional tangent space for 11D supergravity, we make explicit here its integration to a (super-Lie) group. This is equipped with a left-invariant extension of the ''decomposed'' M-theory 3-form, such that it constitutes the Kleinian space on which super-exceptional spacetimes are to be locally modeled as Cartan geometries. As a simple but consequential application, we highlight how to describe lattice subgroups $\mathbb{Z}^{k \leq 528}$ of the hidden M-group that allow to toroidially compactify also the ''hidden'' dimensions of a super-exceptional spacetime, akin to the familiar situation in topological T-duality. In order to deal with subtleties in these constructions, we (i) provide a computer-checked re-derivation of the ''decompose'' M-theory 3-form, and (ii) present a streamlined conception of super-Lie groups, that is both rigorous while still close to physics intuition and practice. Thereby this article highlights modernized super-Lie theory along the example of the hidden M-algebra, with an eye towards laying foundations for super-exceptional geometry. Among new observations is the dimensional reduction of the hidden M-algebra to a ''hidden IIA-algebra'' which in a companion article we explain as the exceptional extension of the T-duality doubled super-spacetime. |
| title | The Hidden M-Group |
| topic | High Energy Physics - Theory Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2411.11963 |