Generalised geometry, eleven dimensions and E11

Abstract

We construct the non-linear realisation of E11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restricted their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.

17 pages, Trivial typos corrected in version one and a substantial note added which gives the equation of motion relating the gravity field to its dual

References in corpus (13)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Supergravity as Generalised Geometry I: Type II Theories
• The E_{11} origin of all maximal supergravities
• SO(5,5) duality in M-theory and generalized geometry
• Generalized complex geometry
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• E11, generalised space-time and IIA string theory
• The E(11) origin of all maximal supergravities - the hierarchy of field-strengths
• E11, generalised space-time and IIA string theory; the R-R sector
• Local E(11)
• E(7(7)) and d=11 supergravity

Cited by in corpus (40)

• Exploring Double Field Theory
• Gauged Double Field Theory
• Extended geometry and gauged maximal supergravity
• Covariant action for a string in doubled yet gauged spacetime
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• U-geometry : SL(5)
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• The Geometry, Branes and Applications of Exceptional Field Theory
• E11 in 11D
• U-duality extension of Drinfel'd double
• Beyond E11
• IIB Supergravity and the E6(6) covariant vector-tensor hierarchy
• On supersymmetric E11 exceptional field theory
• E11, generalised space-time and equations of motion in four dimensions
• E11 must be a symmetry of strings and branes
• A brief review of E theory
• E8 duality and dual gravity
• Timelike U-dualities in Generalised Geometry
• Generalised Space-time and Gauge Transformations
• Exceptional geometry and Borcherds superalgebras
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5
• E11, Romans theory and higher level duality relations
• U-gravity : $\mathbf{SL}(N)$
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• Generalised vielbeins and non-linear realisations
• E11 and exceptional field theory
• On the different formulations of the E11 equations of motion
• E11 and the non-linear dual graviton
• Fermionic T-duality and U-duality in type II supergravity
• U-duality in three and four dimensions
• Dual gravity and E11
• An E11 invariant gauge fixing
• Gauged Supergravities and the Physics of Extra Dimensions
• Unfolding $E_{11}$
• Gravitational Coset Models
• Reductions of Exceptional Field Theories
• Dualized Gravity beyond Linear Approximation