In theoretical physics, the dual graviton is a hypothetical elementary particle that is a dual of the graviton under electric-magnetic duality predicted by some formulations of supergravity in eleven dimensions.
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The dual graviton was first hypothesized in 1980. It was theoretically modeled in 2000s, which was then predicted in eleven-dimensional mathematics of SO(8) supergravity in the framework of electric-magnetic duality. It again emerged in the E11 generalized geometry in eleven dimensions, and the E7 generalized vielbeine-geometry in eleven dimensions. While there is no local coupling between graviton and dual graviton, the field introduced by dual graviton may be coupled to a BF model as non-local gravitational fields in extra dimensions.
Dual linearized gravityEdit
The dual formulations of linearized gravity are described by a mixed Young symmetry tensor , the so-called dual graviton, in any spacetime dimension D > 4 with the following characters:
where square brackets show antisymmetrization.
For 5-D spacetime, the spin-2 dual graviton is described by the Curtright field . The symmetry properties imply that
where is defined as
and the gauge symmetry of the Curtright field is
They fulfill the following Bianchi identities
where is the 5-D spacetime metric.
Dual graviton coupling with BF theoryEdit
Here, is the curvature form, and is the background field.
In principle, it should similarly be coupled to a BF model of gravity as the linearized Einstein–Hilbert action in D > 4:
In similar manner while we define gravitomagnetic and gravitoelectic for the graviton, we can define electric and magnetic fields for the dual graviton. There are the following relation between the gravitoelectic field and gravitomagnetic field of the graviton and the gravitoelectic field and gravitomagnetic field of the dual graviton :
where denotes the Hodge dual.
Dual graviton in conformal gravityEdit
The free (4,0) conformal gravity in D = 6 is defined as
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