Abstract
Double Field Theory (DFT) and Exceptional Field Theory (EFT), collectively called ExFTs, have proven to be a remarkably powerful new framework for string and M-theory. Exceptional field theories were constructed on a case by case basis as often each EFT has its own idiosyncrasies. Intuitively though, an En − 1(n − 1) EFT must be contained in an En(n) ExFT. In this paper we propose a generalised Kaluza-Klein ansatz to relate different ExFTs. We then discuss in more detail the different aspects of the relationship between various ExFTs including the coordinates, section condition and (pseudo)-Lagrangian densities. For the E8(8) EFT we describe a generalisation of the Mukhi-Papageorgakis mechanism to relate the d = 3 topological term in the E8(8) EFT to a Yang-Mills action in the E7(7) EFT.
Highlights
This was not for the full exceptional field theory but just for the extended space and did not consider alternative reductions. We extend these works by examining a host of Exceptional Field Theory (EFT)-to-EFT reductions
Whilst each EFT is constructed in the same way each theory ends up with rather distinct features, necessitating that EFT-to-EFT reductions be treated on a case-by-case basis
The Y -tensor in E8(8) EFT is not sufficient to close the generalised diffeomorphisms, requiring an extra gauge transformation to ensure closure and it is not obvious what happens to this extra gauge transformation if we reduce to E7(7) EFT
Summary
Throughout this paper, an EFT-to-EFT reduction should be understood as a spontaneous symmetry breaking from an En(n) EFT to an En−1(n−1) EFT when there is a generalised isometry present. Gμν is a metric on the external space and AμM is the first level of a tensor hierarchy that is to be modified by higher degree p-form fields (represented by the ellipsis) as required. The latter acts as a gauge field for the generalised Lie derivative. The dynamics of the EFT are constructed from terms that are invariant under both the (internal) generalised diffeomorphisms and external (conventional) diffeomorphisms and requiring reduction to the action of 11-dimensional supergravity upon imposing the section constraint. There is only one inequivalent solution to the DFT section condition
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