We construct a background for M-theory that is moduli free. This background is then shown to be related to a topological phase of the E 8(8) exceptional field theory (ExFT). The key ingredient in the construction is the embedding of non-Riemannian geometry in ExFT. This allows one to describe non-relativistic geometries, such as Newton-Cartan or Gomis-Ooguri-type limits, using the ExFT framework originally developed to describe maximal supergravity. This generalises previous work by Morand and Park in the context of double field theory.

We study how exotic branes, i.e. branes whose tensions are proportional to g −α s , with α > 2, are realised in Exceptional Field Theory (EFT). The generalised torsion of the Weitzenböck connection of the SL(5) EFT which, in the language of gauged supergravity describes the embedding tensor, is shown to classify the exotic branes whose magnetic fluxes can fit into four internal dimensions. By analysing the weight diagrams of the corresponding representations of SL (5) we determine the U-duality orbits relating geometric and nongeometric fluxes. As a further application of the formalism we consider the Kaluza-Klein monopole of 11D supergravity and rotate it into the exotic 6 (3,1) -brane.

In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called 'exotic branes'-low codimension objects with highly nonperturbative tensions, scaling as g α s for α ≤ −3. We argue that their intimate link with these duality transformations make them an ideal object of study using the general framework of Double Field Theory (DFT) and Exceptional Field Theory (EFT)-collectively referred to as ExFT. Parallel to the theme of dualities, we also stress that these theories unify known solutions in string-and M-theory into a single solution under ExFT. We argue that not only is there a natural unifying description of the lowest codimension objects, many of these exotic states require this formalism as a consistent supergravity description does not exist.

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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 E n−1(n−1) EFT must be contained in an E n(n) ExFT but how this works has been unclear since different EFTs are not related by reductions but by rearranging degrees of freedom. 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 E 8(8) EFT we describe a generalisation of the Mukhi -Papageorgakis mechanism to relate the d = 3 topological term in the E 8(8) EFT to a Yang-Mills action in the E 7(7) EFT. 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.