D4-D8 brane bound state




bound states of D4-branes with D8-branes. A special case of the general phenomenon of Dp-D(p+4)-brane bound states.


As a black brane

As a black brane supergravity solution: Brandhuber-Oz 99, Nastase 03, Sec. 2 and 3, BSU 09, Van Pol 15, Sec 5, Dibitetto-Petri 18

As geometric engineering of QCD

The D4-D8 system is the intersecting D-brane model underlying the Witten-Sakai-Sugimoto model for holographic QCD

graphics grabbed from Erlich 09, section 1.1

graphics grabbed from Rebhan 14

As instantons on the D8-brane

Generally, due to the higher WZW term D p+4C p+1FF\propto \int_{D_{p+4}} C_{p+1} \wedge \langle F \wedge F \rangle in the Green-Schwarz sigma model for D(p+4)-branes, Yang-Mills instantons in the Chan-Paton gauge field on D(p+4)D (p+4)-branes are equivalently Dp-D(p+4)-brane bound states (see e.g. Polchinski 96, 5.4, Tong 05, 1.4).

In terms of holographic QCD as above these instantons correspond to baryon-bound states (Sakai-Sugimoto 04, 5.7).

graphics grabbed from Sugimoto 16

brane intersections/bound states/wrapped branes

S-duality\,bound states:



As black brane solutions


As black brane supergravity-solutions:

  • Andreas Brandhuber, Yaron Oz, The D4-D8 Brane System and Five Dimensional Fixed Points, Phys.Lett. B460:307-312, 1999 (arXiv:hep-th/9905148)

  • Horatiu Nastase, Sections 2, 3 of: On Dp-Dp+4 systems, QCD dual and phenomenology (arXiv:hep-th/0305069)

  • Pierre Binetruy, Misao Sasaki, Kunihito Uzawam, Dynamical D4-D8 and D3-D7 branes in supergravity, Phys. Rev. D80:026001, 2009 (arXiv:0712.3615)

  • Oren Bergman, Diego Rodriguez-Gomez, Section 2.3 of: 5d quivers and their AdS 6AdS_6 duals, J. High Energ. Phys. (2012) 2012: 171 (arXiv:1206.3503)

  • Bert Van Pol, Section 5 of: Aspects of D-branes in supergravity, thesis 2015 (pdf, pdf)

  • Giuseppe Dibitetto, Nicolò Petri, Surface defects in the D4-D8 brane system, J. High Energ. Phys. (2019) 2019: 193 (arXiv:1807.07768)

With D2/D6-defects realizing AdS 3/CFT 2AdS_3/CFT_2

black\;D4-D8-brane bound states in massive type IIA string theory, with defect D2-D6-brane bound states inside them realizing AdS3-CFT2 “inside” AdS7-CFT6:

  • Giuseppe Dibitetto, Nicolò Petri, Surface defects in the D4 − D8 brane system, JHEP 01 (2019) 193 (arxiv:1807.07768)

  • Giuseppe Dibitetto, Nicolò Petri, AdS 3AdS_3 vacua and surface defects in massive IIA (arxiv:1904.02455)

As geometric engineering of QCD

With application to geometric engineering of QCD (“holographic QCD”, such as the Witten-Sakai-Sugimoto model):


  • Yolanda Lozano, Section 2 of: Hints on 5d Fixed Point Theories from Non-Abelian T-duality, IFT 2014 (slides pdf, pdf)

As a model for baryons:

Among review of the Witten-Sakai-Sugimoto model:

  • Joshua Erlich, How Well Does AdS/QCD Describe QCD?, Int. J. Mod. Phys.A25:411-421,2010 (arXiv:0908.0312)

  • Anton Rebhan, The Witten-Sakai-Sugimoto model: A brief review and some recent results, 3rd International Conference on New Frontiers in Physics, Kolymbari, Crete, 2014 (arXiv:1410.8858)

General DpD p-D(p+4)D(p+4)-brane bound states

The argument that Yang-Mills instantons in the Chan-Paton gauge field on a D(p+4)-brane are equivalent to Dp-D(p+4) brane bound states goes back to

Review is in:

Discussion specifically of D0-D4-brane bound states:

with emphasis to the resulting configuration spaces of points, as in

Discussion specifically of D1-D5-brane bound states

Last revised on June 1, 2020 at 14:16:09. See the history of this page for a list of all contributions to it.