nLab dual graviton

Contents

Context

Gravity

gravity, supergravity

Formalism

Definition

Einstein-Hilbert action, Einstein's equations, general relativity
- first-order formulation of gravity, D'Auria-Fre formulation of supergravity
- gravity as a BF-theory, Plebanski formulation of gravity, teleparallel gravity

Spacetime configurations

Properties

Spacetimes

black hole spacetimes	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild spacetime	Kerr spacetime
positive charge	Reissner-Nordstrom spacetime	Kerr-Newman spacetime

black hole spacetimes with dark energy	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild-de Sitter spacetime	Kerr-de Sitter spacetime
positive charge	Reissner-Nordström-de Sitter spacetime	Kerr-Newman-de Sitter spacetime

wormhole spacetimes	vanishing angular momentum
vanishing charge	Schwarzschild wormhole
positive charge	Reissner-Nordström wormhole

Quantum theory

quantum gravity
- graviton, gravitino
- string theory

Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

photon - electromagnetic field (abelian Yang-Mills field)
W, Z, B-boson - electroweak field (Yang-Mills field)
gluon - strong nuclear force (Yang-Mills field)
graviton - field of gravity
infraparticle

scalar bosons

Higgs boson, inflaton (scalar field)

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the standard model of particle physics:
generation of fermions	1st generation	2nd generation	3d generation
quarks ( $q$ )
up-type	up quark ( $u$ )	charm quark ( $c$ )	top quark ( $t$ )
down-type	down quark ( $d$ )	strange quark ( $s$ )	bottom quark ( $b$ )
leptons
charged	electron	muon	tauon
neutral	electron neutrino	muon neutrino	tau neutrino

bound states:
mesons	light mesons: pion ( $u d$ ) ρ-meson ( $u d$ ) ω-meson ( $u d$ ) f1-meson a1-meson	strange-mesons: ϕ-meson ( $s \bar s$ ), kaon, K-meson ( $u s$ , $d s$ ) eta-meson ( $u u + d d + s s$ ) charmed heavy mesons*: D-meson ( $u c$ , $d c$ , $s c$ ) J/ψ-meson ( $c \bar c$ )	bottom heavy mesons: B-meson ( $q b$ ) ϒ-meson ( $b \bar b$ )
baryons	nucleons: proton $(u u d)$ neutron $(u d d)$

(also: antiparticles)

effective particles

Goldstone bosons

hadrons (bound states of the above quarks)

meson
- scalar meson
  - σ-meson
  - pion
  - kaon
  - D-meson
  - B-meson
- vector meson
  - ω-meson
  - ρ-meson
  - f1-meson
  - a1-meson
  - b1-meson
  - h1-meson
  - K*-meson
- tensor meson
- quarkonium
  - charmonium
  - ϒ-meson
exotic meson
- XYZ meson
- tetraquark
baryon
- nucleon
  - proton
  - neutron
  - chemical element
    - carbon
    - nitrogen
- Lambda baryon
- pentaquark

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

gravitino - field of supergravity (Rarita-Schwinger field)
gaugino - super Yang-Mills field
gluino

sfermions:

squark

dark matter candidates

WIMP
axion

Exotica

auxiliary fields

Idea
References

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. D 67 (2003) 044010 [arXiv:hep-th/0210278, doi:10.1103/PhysRevD.67.044010]
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: 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]

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)