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Contents

Idea

By dual graviton one refers to the dual of the graviton under electric-magnetic duality (e.g. Curtright 85, Hull 01, Bekaert-Boulanger-Henneaux 02, Godazger-Godazger-Nicolai 13, section 2.2).

Dual gravitons have been considered in particular for manifestly EM-duality-symmetric formulations of supergravity Lagrangians. See for instance (de Wit-Nicolai 13, section 6) and see at 3-d supergravity – possible gaugings.

The spin-2 dual graviton is described by the Curtright field in five spacetime dimensions. Dual graviton can be coupled to topological BF-theory in D = 5 (Bizdadea 09), so it should be also coupled with gravity as a BF theory in extra dimensions D > 4.

References

The dual graviton was maybe first discussed in

• Thomas Curtright, Generalised Gauge Fields, Phys.Lett. B 165:304, 1985 (doi:10.1016/0370-2693(85)91235-3)

then further in

• Chris Hull, Duality in Gravity and Higher Spin Gauge Fields, JHEP 0109:027, 2001 (arXiv:hep-th/0107149)

• Xavier Bekaert, Nicolas Boulanger, Marc Henneaux, Consistent deformations of dual formulations of linearized gravity: A no-go result, Phys. Rev. D67 (2003) 044010 (arXiv:hep-th/0210278)

• Bernard de Wit, Hermann Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions (arXiv:1302.6219)

Discussion in the context of E7-exceptional generalized geometry includes

• Hadi Godazgar, Mahdi Godazgar, Hermann Nicolai, Generalised geometry from the ground up, Journal of High Energy Physics February 2014, 2014:75 (arXiv:1307.8295)

Double-dual graviton:

• Marc Henneaux, Victor Lekeu, Amaury Leonard, A note on the double dual graviton (arxiv:1909.12706)

Discussion in terms of $E_{11}$ U-duality:

• Peter West , section N (pp. 19) of of:Generalised geometry, eleven dimensions and $E_{11}$ (arXiv:1111.1642)

• Keith Glennon, Peter West, Gravity, Dual Gravity and $A_1^{+++}$ (arXiv:2004.03363)

• Nicolas Boulanger, Paul P. Cook, Josh A. O’Connor, Peter West, Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra [[arXiv:2208.11501](https://arxiv.org/abs/2208.11501)&rbrack

Coupling with topological BF-theory in

• C. Bizdadea, E. M. Cioroianu, A. Danehkar, M. Iordache, S. O. Saliu, S. C. Sararu, Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model, The European Physical Journal C (Particles and Fields) October 2009, 63:491 (arXiv:0908.2169)