M-theory, exceptional generalised geometry and superpotentials

By P. P. Pacheco, D. Waldram. 2008

279 citations recorded by the source corpus.

We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in eleven-dimensional supergravity. On a d-dimensional background, as first described by Hull, the action of the generalised geometrical O(d,d) symmetry group is replaced in EGG by the exceptional U-duality group E_d(d). The metric and form-field degrees of freedom combine into a single geometrical object, so that EGG naturally describes generic backgrounds with flux, and there is an EGG analogue of the Courant bracket which encodes the differential geometry. Our focus is on the case of seven-dimensional backgrounds with N=1 four-dimensional supersymmetry. The corresponding EGG is the generalisation of a G_2-structure manifold. We show it is characterised by an element \phi in a particular orbit of the 912 representation of E_7(7), which defines an SU(7) (subset of E_7(7)) structure. As an application, we derive the generic form of the four-dimensional effective superpotential, and show that it can be written in a universal form, as a homogeneous E_7(7)-invariant functional of \phi.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d308b905062a3931e176dab976b65129541e03c3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Gauged Supergravities. (2016, background): “This is the case of the extended generalized geometry [132, 133] and exceptional field theory [134–136] Let us get back to the discussion of the effective lower-dimensional supergravity description originating from flux-backgrounds.”
Double field theory: a pedagogical review (2013, methodology): “These include works by Hull [38], Pacheco and Waldram [39], Berman and Perry [40], the E11 programme by West et al [41] and [42, 43].”
A ten-dimensional action for non-geometric fluxes (2011, background): “ﬂuxes should be included [68, 77, 78]. Such ﬂuxes are not contained in GCG, which focuses on the NSNS sector, but they could be described in a framework such as Exceptional Generalized Geometry (EGG) [79, 80, 81, 82, 83], or following [84, 85]. It would be interesting to investigate whether there is”
Generalized geometry and M theory (2010, methodology): “On the route to our final result we make use of the generalized geometry recently described by Hitchin [9] and by Gualtieri [10] and discussed in an M-theory context by Hull [11] and by Pacheco and Waldram [12].”
Extended geometry and gauged maximal supergravity (2013, methodology): “One of them are configurations obeying the section condition (3.18), which implies that the fields only depend on coordinates spanning a 7-dimensional slice of the extended space, therefore allowing to make contact with supergravity and Exceptional Generalized Geometry.”
Supergravity as generalised geometry I: type II theories (2011, background): “In a forthcoming companion paper [8], we define the corresponding structures in the Ed(d) version of generalised geometry [9, 10] relevant to restrictions of eleven-dimensional supergravity to a d-dimensional manifold.”
Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, methodology): “There is an intricate hierarchy of further coupled gauge transformations of Λ and Λ̃, discussed in more detail in [11] and [8] and which formally defines a form of “gerbe” [37].”
Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions (2012, methodology): “The dynamical fields of supergravity are encoded in a metric on the generalised tangent space introduced in [30, 31, 26] of the form(4)”
Duality Symmetric String and M-Theory (2013, background): “ a powerful guiding principle. We then seek a generalised geometry for M-theory in which En replaces the role played by O(n,n). These exceptional generalised geometries have been developedin [15] and [16]. For the generalised tangent bundle E =TM ⊕T∗M we recall that sections consist of oneforms and ”
Background independent action for double field theory (2010, background): “Generalisations of generalised geometry were proposed in [23] and developed in [24] in which O(D,D) was replaced by U-duality groups; see also [33].”
Duality invariant actions and generalised geometry (2011, background): “This is the same metric as in [45, 46, 34] except for the factor of g1/5.”