nLab exceptional tangent bundle

Contents

Contents

Idea

A generalization of the notion of tangent bundle in exceptional generalized geometry.

For 11-dimensional supergravity the bosonic body of its typical fiber is

d1,1 2( d1,1) * 5( d1,1) * \mathbb{R}^{d-1,1} \oplus \wedge^2 (\mathbb{R}^{d-1,1})^\ast \oplus \wedge^5 (\mathbb{R}^{d-1,1})^\ast

where the second summand corresponds to M2-brane charges and the third to M5-brane charges.

This happens to coincide with the bosonic body of the M-theory super Lie algebra, see there for more.

(…)

References

The notion is already recognizable in

via KK-reduction of the “M-algebra”.

It became more widely appreciated under the heading “exceptional generalized geometry” with:

The actual term “exceptional tangent bundle” appears, in the context of exceptional field theory, for instance in

and the term “exceptional tangent space” (or rather “exceptional generalised tangent space”) appears for instance in

Argument that the M-algebra constitutes the maximal (n=11n=11) (super-)exceptional tangent space:

Last revised on November 7, 2024 at 15:07:38. See the history of this page for a list of all contributions to it.