7-dimensional N=2{\cal N}=2 Consistent Truncations using SL(5)\mathrm{SL}(5) Exceptional Field Theory

We show how to construct seven-dimensional half-maximally supersymmetric consistent truncations of 11-/10-dimensional SUGRA using $\mathrm{SL}(5)$ exceptional field theory. Such truncations are defined on generalised $\mathrm{SU}(2)$-structure manifolds and give rise to seven-dimensional half-maximal gauged supergravities coupled to $n$ vector multiplets and thus with scalar coset space $\mathbb{R}^+ \times \mathrm{O}(3,n)/\mathrm{O}(3)\times\mathrm{O}(n)$. The consistency conditions for the truncation can be written in terms of the generalised Lie derivative and take a simple geometric form. We show that after imposing certain "doublet" and "closure" conditions, the embedding tensor of the gauged supergravity is given by the intrinsic torsion of generalised $\mathrm{SU}(2)$-connections and automatically satisfies the linear constraint of seven-dimensional half-maximal gauged supergravities, as well as the quadratic constraint when the section condition is satisfied.Comment: 46 pages; v2: minor changes, published versio

Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds

We introduce a magnetic analogue of the seven-dimensional nonassociative octonionic R-flux algebra that describes the phase space of M2-branes in four-dimensional locally non-geometric M-theory backgrounds. We show that these two algebras are related by a Spin(7) automorphism of the 3-algebra that provides a covariant description of the eight-dimensional M-theory phase space. We argue that this algebra also underlies the phase space of electrons probing a smeared magnetic monopole in quantum gravity by showing that upon appropriate contractions, the algebra reduces to the noncommutative algebra of a spin foam model of three-dimensional quantum gravity, or to the nonassociative algebra of electrons in a background of uniform magnetic charge. We realise this set-up in M-theory as M-waves probing a delocalised Kaluza-Klein monopole, and show that this system also has a seven-dimensional phase space. We suggest that the smeared Kaluza-Klein monopole is non-geometric because it cannot be described by a local metric. This is the magnetic analogue of the local non-geometry of the R-flux background and arises because the smeared Kaluza-Klein monopole is described by a U(1)-gerbe rather than a U(1)-fibration.Comment: 19 pages, 2 figures; v2: dimensionful factors corrected throughout, exposition improved; Final version to be published in JHE

The Information Metric on the moduli space of instantons with global symmetries

In this note we revisit Hitchin's prescription \cite{Hitchin} of the Fisher metric as a natural measure on the moduli space of instantons that encodes the space-time symmetries of a classical field theory. Motivated by the idea of the moduli space of supersymmetric instantons as an emergent space in the sense of the gauge/gravity duality, we extend the prescription to encode also global symmetries of the underlying theory. We exemplify our construction with the instanton solution of the $\mathbb{CP}^{N}$ sigma model on $\mathbb{R}^{2}$.Comment: 5 pages, no figures, sorr

Open-String Non-Associativity in an R-flux Background

We derive the commutation relations for open-string coordinates on D-branes in non-geometric background spaces. Starting from D0-branes on a three-dimensional torus with H-flux, we show that open strings with end points on D3-branes in a three-dimensional R-flux background exhibit a non-associative phase-space algebra, which is similar to the non-associative R-flux algebra of closed strings. Therefore, the effective open-string gauge theory on the D3-branes is expected to be a non-associative gauge theory. We also point out differences between the non-associative phase space structure of open and closed strings in non-geometric backgrounds, which are related to the different structure of the world-sheet commutators of open and closed strings.Comment: 29 pages; v2: added section 3.5, minor changes; v3: published version, clarifications added in sections 3 and 4, added appendix B.

A geometric formulation of exceptional field theory

We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with $\mathrm{SL}(5)\times\mathbb{R}^+$-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the $\mathrm{SL}(5)\times\mathbb{R}^+$-structure is not locally flat.Comment: 46 page