nLab color branes and flavor branes



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)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
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)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



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)
(flavor-hidden local symmetry)

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 c1N_c \gg 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.


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;


    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


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



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 June 14, 2024 at 08:22:22. See the history of this page for a list of all contributions to it.