Reductions of exceptional field theories

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 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.

The Geometry, Branes and Applications of Exceptional Field Theory

“…The theory is complete for all the finite exceptional groups and there has been significant progress for the infinite dimensional case of E 9 [50,51] as well as attempts [52] at the ultimate E 11 theory proposed by West and collaborators [37] (but so far relatively little progress on the intermediate case of E 10 [314]). Understanding how different ExFTs with different groups are related is still not completely understood, despite the provisional work in [315]. The development of the infinite dimensional cases will no doubt continue and one imagines that the various technical difficulties will be overcome as we understand how different ExFTs are embedded in each other.…”

S-duality and the double copy

“…As we noted in section 3.9, the Kerr-Schild form in double field theory involves more than one gauge field -for example, two Maxwell fields in the case where there is a Kalb-Ramond field as well as the metric. For the string in five dimensions the B field can indeed be simply constructed from two Maxwell gauge fields; See [76,158] for a exceptional field theoretic formulation of the Kerr-Schild double copy. One approach following these ideas is to use a DFT or EFT generalised Killing vector as the basis for generating gauge field strengths in the extended space to express the DFT equations.…”

“…Since the publication of the results in this section, a formulation of Kerr-Schild double copy for exceptional field theory has been obtained in [76,158]; See [159] for a review on exceptional field theory.…”

F-theory with worldvolume sectioning

“…(Reductions of only the massless part of the target space theory ("F-gravity") but for more general U-duality groups were studied in [18].) JHEP04(2021)022…”