E9 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 infinitedimensional 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.

On supersymmetric E11 exceptional field theory

“…So far, E n exceptional field theories have been constructed explicitly for n = 6, 7, 8 in [2][3][4] and in [1,[30][31][32][33] for smaller n. The cases beyond n = 8 involve infinite dimensional groups and bring in formidable new challenges. A dent has been made recently in the case of E 9 [34]. The present paper studies the case of E 11 .…”

Reductions of exceptional field theories

“…Then the generalised Kaluza-Klein vectors can be related to each other as 12) and it is then tempting to write this in term of the Y-tensor as follows: . In order to invert this generalised KK ansatz, we note that we may diagonalise the matrixMMN as follows:MPQ…”

“…i d.s.berman@qmul.ac.uk ii r.otsuki@qmul.ac.uk 1 We have been explicit in specifying the continuous groups as they are not quite the discrete T-and U-duality groups. We shall henceforth drop the R and leave it implicit (see [1] for a discussion of how these dualities appear in ExFTs).2 See also [12,13] for progress on the n = 9 case (the first instance where the extended spacetime is infinite-dimensional). 3 See also [22] which studied the relation between the M-theory and Type IIB solutions of the same EFT.…”

“…2 See also [12,13] for progress on the n = 9 case (the first instance where the extended spacetime is infinite-dimensional). 3 See also [22] which studied the relation between the M-theory and Type IIB solutions of the same EFT.…”

Supergravity Fluxes and Generalised Geometry

“…[] in the context of exceptional field theory. For the purposes of our discussion here, we will restrict to the cases where the external space has dimension at least four, though see [] for recent studies which go beyond this.…”