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M-theory, exceptional generalised geometry and superpotentials

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Title: M-theory, exceptional generalised geometry and superpotentials
Authors: Pacheco, PP
Waldram, D
Item Type: Journal Article
Abstract: 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 Ed(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 G2-structure manifold. We show it is characterised by an element phgr in a particular orbit of the 912 representation of E7(7), which defines an SU(7) ⊂ E7(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 E7(7)-invariant functional of phgr.
Issue Date: 25-Sep-2008
Date of Acceptance: 12-Sep-2008
URI: http://hdl.handle.net/10044/1/52500
DOI: https://dx.doi.org/10.1088/1126-6708/2008/09/123
ISSN: 1029-8479
Publisher: IOP Science
Journal / Book Title: Journal of High Energy Physics
Volume: 9
Copyright Statement: ©2008 IOP Publishing Ltd.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/D047463/1
Keywords: Science & Technology
Physical Sciences
Physics, Particles & Fields
Physics
PHYSICS, PARTICLES & FIELDS
flux compactifications
differential and algebraic geometry
M-theory
string duality
HITCHIN FUNCTIONALS
TOPOLOGICAL STRINGS
D=11 SUPERGRAVITY
MIRROR SYMMETRY
COMPACTIFICATIONS
MANIFOLDS
DUALITY
INVARIANCE
CHARGES
SPACE
hep-th
math.DG
01 Mathematical Sciences
02 Physical Sciences
Nuclear & Particles Physics
Notes: archiveprefix: arXiv primaryclass: hep-th reportnumber: IMPERIAL-TP-08-DW-01 slaccitation: %%CITATION = ARXIV:0804.1362;%%
Publication Status: Published
Article Number: 123
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences



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