nLab D4-D8 brane bound state

Idea

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

Properties

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 $\propto \int_{D_{p+4}} C_{p+1} \wedge \langle F \wedge F \rangle$ in the Green-Schwarz sigma model for D(p+4)-branes, Yang-Mills instantons in the Chan-Paton gauge field on $D (p+4)$-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

Related entries

brane intersections/bound states/wrapped branes/polarized branes

• D-branes and anti D-branes form bound states by tachyon condensation, thought to imply the classification of D-brane charge by K-theory

• intersecting D-branes/fuzzy funnels:

  • Dp-D(p+2)-brane bound state and Yang-Mills monopoles

    • D0-D2 brane bound state

    • D1-D3 brane bound state

    • D2-D4 brane bound state

    • D3-D5 brane bound state

    • D4-D6 brane bound state

    • D6-D8-brane bound state

  • Dp-D(p+4)-brane bound state and Yang-Mills instantons

    • D0-D4 brane bound state

    • D1-D5 brane bound state

    • D2-D6 brane bound state

    • D3-D7 brane bound state

    • D4-D8 brane bound state

    • D5-D9 brane bound state

      small instanton

• Dp-D(p+6) brane bound state

  • D0-D6 brane bound state

  • D1-D7 brane bound state

  • D2-D8 brane bound state

• NS5-D4-D2 bound states

• Hanany-Witten effect

S-duality$\,$bound states:

• (p,q)-string

• (p,q)5-branes

• string network

• 5-brane web

intersecting$\,$M-branes:

• M5-MO9 brane bound state

• M2-M5 brane bound state

  • M-string, E-string

• membrane triple junction

References

As black brane solutions

General

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 $AdS_6$ 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)

• Minwoo Suh, D4-D8-branes wrapped on a manifold with non-constant curvature (arXiv:2108.08326)

With D2/D6-defects realizing $AdS_3/CFT_2$

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, $AdS_3$ 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):

• David Morrison, Nathan Seiberg, Extremal Transitions and Five-Dimensional Supersymmetric Field Theories, Nucl. Phys.B483:229-247, 1997 (arXiv:hep-th/9609070)

• Nastase 03, Sec. 5

• Hee-Cheol Kim, Sung-Soo Kim, Kimyeong Lee, 5-dim Superconformal Index with Enhanced En Global Symmetry, JHEP 1210 (2012) 142 (arXiv:1206.6781)

• Chiung Hwang, Joonho Kim, Seok Kim, Jaemo Park, General instanton counting and 5d SCFT (arxiv:1406.6793)

Review:

• 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:

• Tadakatsu Sakai, Shigeki Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys.113:843-882, 2005 (arXiv:hep-th/0412141)

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 $D p$-$D(p+4)$-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

• Edward Witten, Small Instantons in String Theory, Nucl. Phys. B460:541-559, 1996 (arXiv:hep-th/9511030)

• Michael Douglas, Gauge Fields and D-branes, J. Geom. Phys. 28 (1998) 255-262 (arXiv:hep-th/9604198)

Review is in:

• Joseph Polchinski, Section 5.4 of: TASI Lectures on D-Branes (arXiv:hep-th/9611050)

• David Tong, Section 1.4 of TASI Lectures on Solitons (hep-th/0509216)

Discussion specifically of D0-D4-brane bound states:

• Cumrun Vafa, Instantons on D-branes, Nucl. Phys. B463 (1996) 435-442 (arXiv:hep-th/9512078)

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

• Cumrun Vafa, Edward Witten, Section 4.1 of: A Strong Coupling Test of S-Duality, Nucl. Phys. B431:3-77, 1994 (arXiv:hep-th/9408074)

Discussion specifically of D1-D5-brane bound states

• Neil Lambert, D-brane Bound States and the Generalised ADHM Construction, Nucl. Phys. B519 (1998) 214-224 (arXiv:hep-th/9707156)