$SL(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory: An Action for F-Theory

Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times {\mathbb{R}}^{+}$ together with its action is presented. Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to Type IIB supergravity and F-theory. Thus $SL(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory contains both F-theory and M-theory in a single 12-dimensional formalism.