Contents

### Context

#### Fields and quanta

fields and particles in particle physics

and in the 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

hadrons (bound states of the above quarks)

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## Idea

The idea of Kaluza-Klein theory has traditionally been applied mostly to “color physics”, such as in attempts to realize the color charges of quantum chromodynamics (quarks and gluons) as a Kaluza-Klein compactification of heterotic supergravity (see for instance at string phenomenologyheterotic models). The success of this approach remains somewhat elusive (see also at landscape of string theory vacua).

Alternatively, Kaluza-Klein theory may be considered for “flavor physics” to produce the charges of flavor-“hidden local symmetries”, namely the baryons and mesons, respectively, hence the hadrons of quantum hadrodynamics. In terms of geometric engineering of QFT via intersecting D-brane models this means to consider gauge theory on flavor branes (instead of on color branes), such as in the Witten-Sakai-Sugimoto model of holographic QCD.

Indeed, the experimentally observed mesons appear in towers of increasing mass (“higher resonances”), which may usefully be identified as a Kaluza-Klein tower of the single gauge boson of an SU(2)-D=5 Yang-Mills theory (Son-Stephanov 03).

Moreover, the pion field appears as the gauge 0-mode of this tower, right away in its solitonic incarnation as the Skyrmion-excitation in 4d, hence reflecting baryons. (This phenomenon is secretly the old theorem of Atiyah-Manton 89, as explained from the modern perspective of holographic QCD in Sutcliffe 10, Sutcliffe 15).

Various qualitative phenomena of the phenomenology of quantum hadrodynamics find a natural explanation in hadron Kaluza-Klein theory this way, notably:

1. hidden local symmetry itself (by the very KK-reduction of a gauge theory)

2. vector meson dominance (as discussed there)

3. QCD sum rules (…)

4. (…)

In terms of string phenomenology, the flavor brane-D=5 Yang-Mills theory which gives quantum hadrodynamics this way naturally arises on D4/D8-brane intersections in the Witten-Sakai-Sugimoto model (Sakai-Sugimoto 04, Sakai-Sugimoto 05) or else on M5-branes wrapped on a closed interval (Ivanova-Lechtenfeld-Popov 18)

Already to first approximation, this produces for instance baryon mass spectra with moderate quantitative agreement with experiment (HSSY 07):

graphics grabbed from Sugimoto 16

An extensive review of hadron Kaluza-Klein theory may be found in Rho et al 16.

Strikingly, the experimentally observed hadron-spectrum also exhibits supersymmetry: see at hadron supersymmetry.

## References

### Hadrons as KK-modes of 5d Yang-Mills theory

The suggestion that the tower of observed vector mesons, when regarded as gauge fields of hidden local symmetries of chiral perturbation theory, is reasonably modeled as a Kaluza-Klein tower of D=5 Yang-Mills theory:

That the pure pion-Skyrmion-model of baryons is approximately the KK-reduction of instantons in D=5 Yang-Mills theory is already due to

with a hyperbolic space-variant in

The observation that the result of Atiyah-Manton 89 becomes an exact Kaluza-Klein construction of Skyrmions/baryons from D=5 instantons when the full KK-tower of vector mesons as in Son-Stephanov 03 is included into the Skyrmion model (see also there) is due to

In the Sakai-Sugimoto model of holographic QCD the D=5 Yang-Mills theory of this hadron Kaluza-Klein theory is identified with the worldvolume-theory of D8-flavour branes intersected with D4-branes in an intersecting D-brane model:

Extensive review of this holographic/KK-theoretic-realization of quantum hadrodynamics from D=5 Yang-Mills theory is in:

Via the realization of D4/D8 brane bound states as instantons in the D8-brane worldvolume-theory (see there and there), this relates also to the model of baryons as wrapped D4-branes, originally due to

and further developed in the nuclear matrix model:

More on baryons in the Sakai-Sugimoto model of holographic QCD:

More on mesons in holographic QCD:

• Daniel Ávila, Leonardo Patiño, Melting holographic mesons by cooling a magnetized quark gluon plasma (arXiv:2002.02470)

• Xuanmin Cao, Hui Liu, Danning Li, Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography, Phys. Rev. D 102, 126014 (2020) (arXiv:2009.00289)

• Xuanmin Cao, Songyu Qiu, Hui Liu, Danning Li, Thermal properties of light mesons from holography (arXiv:2102.10946)

• Artur Amorim, Miguel S. Costa, Matti Järvinen, Regge theory in a Holographic dual of QCD in the Veneziano Limit (arXiv:2102.11296)

• R. da Rocha, Information in AdS/QCD: mass spectroscopy of isovector mesons (arXiv:2103.03924)

• Shahin Mamedov, Narmin Nasibova, Temperature dependence of $\rho$ meson-nucleon coupling constant from the soft-wall model (arXiv:2103.10494)

An alternative scenario of derivation of 4d Skyrmions by KK-compactification of D=5 Yang-Mills theory, now on a closed interval, motivated by M5-branes instead of by D4/D8-brane intersections as in the Sakai-Sugimoto model, is discussed in:

following

### History

The late Michael Atiyah, following up on his visionary early work in Atiyah-Manton 89, saw the relevance of further develop hadron Kaluza-Klein theory, and suggested using advanced tools of complex geometry for this purpose; for a reminiscence see

This led to a sequence of visionary but speculative articles, including the following:

The idea here is to try to match patterns in the characteristic classes (Chern classes) of complex surfaces to properties of nuclei.

Created on May 8, 2020 at 08:00:05. See the history of this page for a list of all contributions to it.