Exceptional Field Theory. I. E[subscript 6(6)]-Covariant Form of M-Theory and Type IIB

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We present the details of the recently constructed E 6ð6Þ-covariant extension of 11-dimensional supergravity. This theory requires a 5 þ 27-dimensional spacetime in which the " internal " coordinates transform in the ¯ 27 of E 6ð6Þ. All fields are E 6ð6Þ tensors and transform under (gauged) internal generalized diffeomorphisms. The " Kaluza-Klein " vector field acts as a gauge field for the E 6ð6Þ-covariant " E-bracket " rather than a Lie bracket, requiring the presence of 2-forms akin to the tensor hierarchy of gauged supergravity. We construct the complete and unique action that is gauge invariant under generalized diffeomorphisms in the internal and external coordinates. The theory is subject to covariant section constraints on the derivatives, implying that only a subset of the extra 27 coordinates is physical. We give two solutions of the section constraints: the first preserves GL(6) and embeds the action of the complete (i.e. untruncated) 11-dimensional supergravity; the second preserves GLð5Þ × SLð2Þ and embeds complete type IIB supergravity. As a byproduct, we thus obtain an off-shell action for type IIB supergravity.