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

Last revised on September 17, 2024 at 15:07:22. See the history of this page for a list of all contributions to it.