nLab color branes and flavor branes

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

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

	color charge	flavor charge
gauge bosons	gluons (gauge group-local symmetry)	mesons (flavor-hidden local symmetry)
fermions	quarks	baryons

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 $N_c \gg 1$ black branes while flavor branes are modeled as $N_f \sim 1$ 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:

• hadron supersymmetry

• hadron Kaluza-Klein theory

Related concepts

• probe brane

References

General

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

• Andreas Karch, Emanuel Katz, Adding flavor to AdS/CFT, JHEP 0206:043, 2002 (arxiv:hep-th/0205236)

based on the concept of probe branes due to

• Andreas Karch, Lisa Randall, Section 3 of: Open and Closed String Interpretation of SUSY CFT’s on Branes with Boundaries, JHEP 0106:063, 2001 (arXiv:hep-th/0105132)

Other early discussion:

• Peter Ouyang, Holomorphic D7-Branes and Flavored $\mathcal{N}=1$ Gauge Theories, Nucl. Phys. B699:207-225, 2004 (arXiv:hep-th/0311084)

• Thomas S. Levi, Peter Ouyang, Mesons and Flavor on the Conifold, Phys. Rev. D76:105022, 2007 (arXiv:hep-th/0506021)

• Carlos Nunez, A. Paredes, A.V. Ramallo, Flavoring the gravity dual of $\mathcal{N}=1$ Yang-Mills with probes, JHEP 0312:024, 2003 (arXiv:hep-th/0311201)

See also:

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

$SU(2)$-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):

• Abhijit Gadde, Babak Haghighat, Joonho Kim, Seok Kim, Guglielmo Lockhart, Cumrun Vafa, Section 4.2 of: 6d String Chains, J. High Energ. Phys. 2018, 143 (2018) (arXiv:1504.04614, doi:10.1007/JHEP02(2018)143)

• Kantaro Ohmori, Section 2.3.1 of: Six-Dimensional Superconformal Field Theories and Their Torus Compactifications, Springer Theses 2018 (springer:book/9789811330919)

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 $\mathcal{N}=(1,0)$ 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:

• Amihay Hanany, Alberto Zaffaroni, Branes and Six Dimensional Supersymmetric Theories, Nucl.Phys. B529 (1998) 180-206 (arXiv:hep-th/9712145)

• Ilka Brunner, Andreas Karch, Branes at Orbifolds versus Hanany Witten in Six Dimensions, JHEP 9803:003, 1998 (arXiv:hep-th/9712143)

Reviewed in:

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

See also:

• Amihay Hanany, Noppadol Mekareeya, The Small $E_8$ Instanton and the Kraft Procesi Transition, JHEP07 (2018) 098 (arXiv:1801.01129)