Fields and quanta

field (physics)

standard model of particle physics

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonspion (udu d)
rho-meson (udu d)
omega-meson (udu d)
kaon (q u/dsq_{u/d} s)
eta-meson (u u + d d + s s)
B-meson (qbq b)
baryonsproton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)


minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



Given a Kaluza-Klein compactification on a circle principal bundle (X^,g^)(\widehat X, \widehat g), the graviphoton field is the resulting gauge field (electromagnetic field) on the base of the fibration.


If v 5Γ(TX^)v_5 \in \Gamma\big( T\widehat X\big) denotes the vertical vector field which corresponds to the isometric flow along the circle fibers, the graviphoton field, regraded as a Cartan connection differential 1-form on the total space X^\widehat X bundle is the contraction of the metric tensor g^\widehat g with this vector field:

Ag^(v,). A \;\coloneqq\; \widehat g(v,-) \,.


In type IIA string theory

In the duality between M-theory and type IIA string theory, the graviphoton of the KK-compactification is the RR-field potential C 1C_1 of type IIA string theory.

On D4-branes

The graviphoton as the RR-field potential C 1C_1 of type IIA string theory then appears in the higher WZW term on the D4-brane (CGNSW 96 (7.4) APPS97b (51)) as the theta angle in D=5 super Yang-Mills theory:

L D4 WZC 1FF. \mathbf{L}_{D4}^{WZ} \;\propto\; C_1 \wedge \langle F \wedge F\rangle \,.



See also

In string theory

The graviphoton of the duality between M-theory and type IIA string theory, as the RR-field-potential C 1C_1 in the higher WZW term of the D4-brane:

For more see at Green-Schwarz sigma model – References – For D-branes.

Discussion as the theta angle of the Witten-Sakai-Sugimoto model for QCD on D4-branes:

  • Si-wen Li, around (3.1) of The theta-dependent Yang-Mills theory at finite temperature in a holographic description (arXiv:1907.10277)

Last revised on July 25, 2019 at 10:07:12. See the history of this page for a list of all contributions to it.