E 9 exceptional field theory. Part I. The potential

Abstract We construct the scalar potential for the exceptional field theory based on the affine symmetry group E 9. The fields appearing in this potential live formally on an infinite-dimensional extended spacetime and transform under E 9 generalised diffeomorphisms. In addition to the scalar fields expected from D = 2 maximal supergravity, the invariance of the potential requires the introduction of new constrained scalar fields. Other essential ingredients in the construction include the Virasoro algebra and indecomposable representations of E 9. Upon solving the section constraint, the potential reproduces the dynamics of either eleven-dimensional or type IIB supergravity in the presence of two isometries