The Hidden M-Group
Grigorios Giotopoulos, Hisham Sati, Urs Schreiber

TL;DR
This paper constructs a super-Lie group integrating the hidden M-algebra related to 11D supergravity, enabling modeling of super-exceptional spacetimes and exploring their compactifications, with rigorous mathematical and computational foundations.
Contribution
It explicitly integrates the hidden M-algebra into a super-Lie group and develops a rigorous, physics-inspired framework for super-exceptional geometry and spacetime compactifications.
Findings
Construction of the super-Lie group for the hidden M-algebra.
Explicit computer-checked derivation of the M-theory 3-form.
Description of lattice subgroups enabling toroidal compactification.
Abstract
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 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…
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