Abstract
We construct the scalar potential for the exceptional field theory based on the affine symmetry group E9. The fields appearing in this potential live formally on an infinite-dimensional extended spacetime and transform under E9 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 E9. Upon solving the section constraint, the potential reproduces the dynamics of either eleven-dimensional or type IIB supergravity in the presence of two isometries.
Highlights
Exceptional geometry is a way of unifying the local symmetries of supergravity theories by combining geometric diffeomorphisms with matter gauge transformations into a single so-called generalised Lie derivative [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
As two-dimensional gauged supergravities generically involve a gauging of the RL−1 symmetry [31], it is crucial to construct the E9 potential at ρ = 0, which is invariant under all generalised diffeomorphisms
Since the Fock space notation in (3.15) is different from that used for finite-dimensional symmetry groups, we provide a short translation into index notation using (2.7) and (2.8)
Summary
Exceptional geometry is a way of unifying the local symmetries of supergravity theories by combining geometric diffeomorphisms with matter gauge transformations into a single so-called generalised Lie derivative [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. As two-dimensional gauged supergravities generically involve a gauging of the RL−1 symmetry [31], it is crucial to construct the E9 potential at ρ = 0, which is invariant under all generalised diffeomorphisms Another possible application is the study of non-geometric backgrounds [1, 2, 6, 8]. Our construction does not depend on the details of the group E8 and the expressions we give will be valid for any simple group G and its affine extension G This provides the potential for extended field theories with coordinates in the basic representation of Gthat are invariant under rigid G (R+d RL−1) and Ggeneralised diffeomorphisms.
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