An Action for F-theory: SL(2)× R Exceptional Field Theory

We construct the 12-dimensional exceptional field theory associated to the group SL(2)× R. 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 F-theory. Thus SL(2) × R exceptional field theory contains both F-theory and M-theory in a single 12-dimensional formalism. 1 [email protected] 2 [email protected] [email protected] 4 [email protected]