Locally non-geometric fluxes and missing momenta in M-theory

Abstract

We use exceptional field theory to describe locally non-geometric spaces of M-theory of more than three dimensions. For these spaces, we find a new set of locally non-geometric fluxes which lie in the R-R sector in the weak-coupling limit and can typically be characterised by mixed symmetry tensors. These spaces thus provide new examples of non-geometric backgrounds which go beyond the NS-NS sector of string theory. Starting from twisted tori we construct duality chains that lead to these new non-geometric backgrounds and we show that, just as in the four-dimensional case, there are missing momenta associated to the mixed symmetry tensors.

Fluxes in exceptional field theory and threebrane sigma-models

“…Finally, let us compare our results with the SL(5) fluxes described in [4,10], where a group theoretical derivation in terms of SL(5) representation theory was used. Based on the embedding tensor formalism for gaugings of seven-dimensional maximal supergravity [58], the relevant representations of SL(5) are 15 ⊕ 40 ⊕ 10, and therefore the fluxes should exhaust these representations.…”

“…Motivated by Scherk-Schwarz reductions of M-theory on twisted tori, studied in detail in [37], we can choose ρ i j to be equal to the components of a globally defined coframe E i j (X) for a twisted torus. 9 The simplest example, but by no means the only one, is to take a twisted 4-torus which is a trivial circle bundle over the three-dimensional Heisenberg nilmanifold, see for example [4,[6][7][8][9][10]. Then T i jk is simply given by (4.15) and it is constant, corresponding to the structure constants of the associated nilpotent Lie algebra.…”

“…In the context of M-theory, the full set of fluxes for its seven-dimensional compactifications 1 was determined in [4] using SL(5) exceptional field theory [5], and studied further also for dimensions up to seven in [6][7][8][9][10]. The latter is the M-theory analogue of double field theory [11][12][13], in that both theories are proposals for a duality-invariant formulation, be it T-duality in the string theory case or U-duality in the M-theory case.…”

An introduction to nonassociative physics

“…where the radius λ of the circle fibres geometrizes the string coupling g s . The lifts of the threedimensional constant R-flux backgrounds to locally non-geometric backgrounds of M-theory was considered for compactifications to four dimensions in [60] and to higher dimensions in [105]; we focus here on the former lift. One starts from a double T-duality taking the Heisenberg nilmanifold M =T 3 to the R-flux background:…”

Uplifts of maximal supergravities and transitions to non-geometric vacua

“…The interpretation of embedding tensor components in terms of fluxes in equation (6.1) assumed this choice of solution of the section constraint. The parameter θ 77 is usually considered to be a locally geometric flux on a torus (see for instance [69] and more recently [70]). However, notice that the combination of θ (mn) flux with seven-form flux can also be interpreted geometrically as curvature of an internal sphere or hyperboloid [23].…”