color branes and flavor branes



String theory

Fields and quanta

field (physics)

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:
mesonspion (udu d)
rho-meson (udu d)
omega-meson (udu d)
kaon (q u/dsq_{u/d} s)
eta-meson (u u + d d + s s)
B-meson (qbq b)
baryonsproton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadron (bound states of the above quarks)


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).


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

Created on March 26, 2020 at 05:24:18. See the history of this page for a list of all contributions to it.