fields and particles in particle physics
and in the standard model of particle physics:
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)
hadrons (bound states of the above quarks)
minimally extended supersymmetric standard model
bosinos:
dark matter candidates
Exotica
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 phenomenology – heterotic 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.
color charge | flavor charge | |
---|---|---|
gauge bosons | gluons (gauge group-local symmetry) | mesons (flavor-hidden local symmetry) |
fermions | quarks | baryons |
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:
hidden local symmetry itself (by the very KK-reduction of a gauge theory)
vector meson dominance (as discussed there)
QCD sum rules (…)
(…)
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.
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
Paul Sutcliffe, Skyrmions, instantons and holography, JHEP 1008:019, 2010 (arXiv:1003.0023)
Paul Sutcliffe, Holographic Skyrmions, Mod. Phys. Lett. B29 (2015) no. 16, 1540051 (spire:1383608, doi:10.1142/S0217984915400515)
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:
Tadakatsu Sakai, Shigeki Sugimoto, section 5.2 of Low energy hadron physics in holographic QCD, Prog.Theor.Phys.113:843-882, 2005 (arXiv:hep-th/0412141)
Tadakatsu Sakai, Shigeki Sugimoto, section 3.3. of More on a holographic dual of QCD, Prog.Theor.Phys.114:1083-1118, 2005 (arXiv:hep-th/0507073)
Hiroyuki Hata, Tadakatsu Sakai, Shigeki Sugimoto, Shinichiro Yamato, Baryons from instantons in holographic QCD, Prog.Theor.Phys.117:1157, 2007 (arXiv:hep-th/0701280)
Stefano Bolognesi, Paul Sutcliffe, The Sakai-Sugimoto soliton, JHEP 1401:078, 2014 (arXiv:1309.1396)
Lorenzo Bartolini, Stefano Bolognesi, Andrea Proto, From the Sakai-Sugimoto Model to the Generalized Skyrme Model, Phys. Rev. D 97, 014024 2018 (arXiv:1711.03873)
Extensive review of this holographic/KK-theoretic-realization of quantum hadrodynamics from D=5 Yang-Mills theory is in:
Mannque Rho, Ismail Zahed (eds.) The Multifaceted Skyrmion, World Scientific, Second edition, 2016 (doi:10.1142/9710)
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
Edward Witten, Baryons And Branes In Anti de Sitter Space, JHEP 9807:006, 1998 (arXiv:hep-th/9805112)
David Gross, Hirosi Ooguri, Aspects of Large $N$ Gauge Theory Dynamics as Seen by String Theory, Phys. Rev. D58:106002, 1998 (arXiv:hep-th/9805129)
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
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:
Michael Atiyah, Nicholas Manton, Bernd Schroers, Geometric Models of Matter, Proceedings of the Royal Society A (arXiv:1108.5151, doi:10.1098/rspa.2011.0616)
Michael Atiyah, Nicholas Manton, Complex Geometry of Nuclei and Atoms, International Journal of Modern Physics AVol. 33, No. 24, 1830022 (2018) (arXiv:1609.02816, doi:10.1142/S0217751X18300223)
Michael Atiyah, Geometric Models of Helium, Modern Physics Letters AVol. 32, No. 14, 1750079 (2017) (arXiv:1703.02532, doi:10.1142/S0217732317500791)
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.