# nLab graviphoton

Contents

### Context

#### Fields and quanta

field (physics)

standard model of particle physics

force field gauge bosons

scalar bosons

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks ($q$)
up-typeup quark ($u$)charm quark ($c$)top quark ($t$)
down-typedown quark ($d$)strange quark ($s$)bottom quark ($b$)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight 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 ($b \bar b$)
baryonsnucleons:
proton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)

solitons

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## Idea

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

## Definition

If $v_5 \in \Gamma\big( T\widehat X\big)$ 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 $\widehat X$ bundle is the contraction of the metric tensor $\widehat g$ with this vector field:

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

## Examples

### 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 $C_1$ of type IIA string theory.

### On D4-branes

The graviphoton as the RR-field potential $C_1$ 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:

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

## References

### General

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