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We present the details of the recently constructed $E_{6(6)}$ covariantextension of 11-dimensional supergravity. This theory requires a 5+27dimensional spacetime in which the `internal' coordinates transform in the$\bar{\bf 27}$ of $E_{6(6)}$. All fields are $E_{6(6)}$ tensors and transformunder (gauged) internal generalized diffeomorphisms. The `Kaluza-Klein' vectorfield acts as a gauge field for the $E_{6(6)}$ covariant `E-bracket' ratherthan a Lie bracket, requiring the presence of two-forms akin to the tensorhierarchy of gauged supergravity. We construct the complete and unique actionthat is gauge invariant under generalized diffeomorphisms in the internal andexternal coordinates. The theory is subject to covariant section constraints onthe derivatives, implying that only a subset of the extra 27 coordinates isphysical. We give two solutions of the section constraints: the first preservesGL(6) and embeds the action of the complete (i.e. untruncated) 11-dimensionalsupergravity; the second preserves GL(5) x SL(2) and embeds complete type IIBsupergravity. As a by-product, we thus obtain an off-shell action for type IIBsupergravity.

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