Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB

Understand

We present the details of the recently constructed $E_{6(6)}$ covariant extension of 11-dimensional supergravity.

• This theory requires a 5+27 dimensional spacetime in which the `internal' coordinates transform in the $\bar{\bf 27}$ of $E_{6(6)}$.
• All fields are $E_{6(6)}$ tensors and transform under (gauged) internal generalized diffeomorphisms.
• The `Kaluza-Klein' vector field acts as a gauge field for the $E_{6(6)}$ covariant `E-bracket' rather than a Lie bracket, requiring the presence of two-forms akin to the tensor hierarchy of gauged supergravity.