nLab
color branes and flavor branes

Contents

Context

String theory

Fields and quanta

fields and particles in particle physics

and in the 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)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
f1-meson
a1-meson
strange-mesons:
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
baryonsnucleons:
proton (uud)(u u d)
neutron (udd)(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:

sfermions:

dark matter candidates

Exotica

auxiliary fields

Contents

Idea

In geometric engineering of quantum field theory in intersecting D-brane models the gauge theory which is thought to appear on coincident D-branes (see at gauge enhancement) may play two different roles:

  1. color – it may be a Yang-Mills theory of an “actual” gauge field (carried by gluons) coupled to color charges (carried by quarks) – like quantum chromodynamics;

  2. flavor – it may be the (“chiral”) gauge theory of a hidden local gauge field (carried by mesons) coupled to flavor charges (carried by baryons) – like quantum hadrodynamics.

In the first case one speaks of color branes, in the second of flavor branes. Typically one indicates the number of coincident such branes with

  1. N cN_c \in \mathbb{N} for the number of color branes, leading (in the absence of orientifolds) to gauge group SU(N c)(N_c);

  2. N fN_f \in \mathbb{N} for the number of flavor branes, leading to flavor-symmetry group (“chiral symmetry”) SU(N f)(N_f) (e.g. isospin for N f=2N_f = 2).

color chargeflavor charge
gauge bosonsgluons
(gauge group-local symmetry)
mesons
(flavor-hidden local symmetry)
fermionsquarksbaryons

In common constructions of holographic QCD in the large-N limit (large number of color charges) in which the AdS/QCD correspondence applies, color branes are modeled as N cggt1N_c \ggt 1 black branes while flavor branes are modeled as N f1N_f \sim 1 probe branes (Karch-Katz 02).

From Ouyang 03, p. 2:

the important feature seems to be that the added branes must be extended along the radial AdS direction; then, volume factors suppress the dynamics of the NN strings on these “flavor branes”, which then contribute states to the gauge theory with global symmetries rather than gauge symmetries.

Examples

Witten-Sakai-Sugimoto model for quantum chromodynamics

For example, in the Witten-Sakai-Sugimoto model for holographic QCD realized on D4-D8 brane intersections, the D4-branes play the role of color branes while the D8-branes play the role of flavor branes.

graphics from Sati-Schreiber 19c

Here we are showing

  1. the color D4-branes;

  2. the flavor D8-branes;

    with

    1. the 5d Chern-Simons theory on their worldvolume

    2. the corresponding 4d WZW model on the boundary

    exhibiting the vector meson fields in the Skyrmion model;

  3. the baryon D4-branes

    (see below at Baryons);

  4. the Yang-Mills monopole D6-branes

    (see at D6-D8-brane bound state);

  5. the NS5-branes (often not considered here).

graphics from Sati-Schreiber 19c

Phenomenology

The geometric engineering of QFT on flavor branes (as in the Witten-Sakai-Sugimoto model) realizes, at least qualitatively, the following experimentall phenomena:

References

General

The concept of flavor branes in the context of holographic QCD properly originates with:

based on the concept of probe branes due to

Other early discussion:

See also:

  • Daniel Arean, Adding flavor on the Higgs branch, Fortsch. Phys. 56:888-894, 2008 (arXiv:0805.3447)

SU(2)SU(2)-flavor symmetry on heterotic M5-branes

Emergence of SU(2) flavor-symmetry on single M5-branes in heterotic M-theory on ADE-orbifolds (in the D=6 N=(1,0) SCFT on small instantons in heterotic string theory):

Argument for this by translation under duality between M-theory and type IIA string theory to half NS5-brane/D6/D8-brane bound state systems in type I' string theory:

Reviewed in:

  • Santiago Cabrera, Amihay Hanany, Marcus Sperling, Section 2.3 of: Magnetic Quivers, Higgs Branches, and 6d 𝒩=(1,0)\mathcal{N}=(1,0) Theories, JHEP06(2019)071, JHEP07(2019)137 (arXiv:1904.12293)

The emergence of flavor in these half NS5-brane/D6/D8-brane bound state systems, due to the semi-infinite extension of the D6-branes making them act as flavor branes:

Reviewed in:

  • Fabio Apruzzi, Marco Fazzi, Section 2.1 of: AdS 7/CFT 6AdS_7/CFT_6 with orientifolds, J. High Energ. Phys. (2018) 2018: 124 (arXiv:1712.03235)

See also:

Last revised on May 19, 2020 at 16:23:01. See the history of this page for a list of all contributions to it.