nLab Dp-D(p+4)-brane bound state

Idea

bound states of Dp-branes with D(p+4)-branes.

Properties

As Yang-Mills instantons in the Chan-Paton gauge field

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).

Examples

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

• D0-D4 brane bound state

• D1-D5 brane bound state

• D4-D8 brane bound state

• M5-MO9 brane bound state

Related concepts

• fuzzy funnel

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

Relation to instantons

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, Branes within Branes, In: Baulieu L., Di Francesco P., Douglas M., Kazakov V., Picco M., Windey P. (eds.) Strings, Branes and Dualities NATO ASI Series (Series C: Mathematical and Physical Sciences), vol 520. Springer, Dordrecht (arxiv:hep-th/9512077, doi:10.1007/978-94-011-4730-9_10)

• 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)

D0-D4-brane bound states

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)

D1-D5-brane bound states

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)

• Emil Martinec, Manifestations of the D1-D5 system, 1999 (pdf)

• A review of the D1/D5 system and five dimensional black hole from supergravity and brane viewpoint (arXiv:hep-th/0002184)

D4-D8-brane bound states

Discussion specifically of D4-D8-brane bound states:

In the Witten-Sakai-Sugimoto model geometrically engineering QCD, where the D4-branes get interpreted as baryons:

• Tadakatsu Sakai, Shigeki Sugimoto, Section 5.7 of: Low energy hadron physics in holographic QCD, Prog. Theor. Phys.113:843-882, 2005 (arXiv:hep-th/0412141)

M5-MO9 brane bound states

Discussion specifically of M5-MO9 brane bound states:

Discussion as Yang-Mills instantons (“small instantons”):

• Andrew Strominger, Heterotic solitons, Nucl. Phys. B343 (1990) 167-184 (doi:10.1016/0550-3213(90)90599-9) Erratum: Nucl. Phys. B353 (1991) 565-565 (doi:10.1016/0550-3213(91)90349-3) (spire:27900)

• Edward Witten, Small Instantons in String Theory, Nucl.Phys.B460:541-559, 1996 (doi:10.1016/0550-3213(95)00625-7)

Discussion as half M5-branes:

• John Huerta, Hisham Sati, Urs Schreiber, Example 2.2.7 of: Real ADE-equivariant (co)homotopy and Super M-branes, CMP (2019) (arXiv:1805.05987, doi:10.1007/s00220-019-03442-3)

• Domenico Fiorenza, Hisham Sati, Urs Schreiber, Section 4 of: Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5 (arXiv:1908.00042)

• Hisham Sati, Urs Schreiber, Section 4.1 of: Equivariant Cohomotopy implies orientifold tadpole cancellation (arXiv:1909.12277)

In solid state physics

Relation of Yang-Mills monopoles as Dp/D(p+2)-brane intersections and Yang-Mills instantons as Dp/D(p+4)-brane intersections to the K-theory classification of topological phases of matter via AdS/CFT duality in solid state physics:

• Koji Hashimoto, Taro Kimura, Band spectrum is D-brane, Progress of Theoretical and Experimental Physics, Volume 2016, Issue 1 (arXiv:1509.04676)

• Charlotte Kristjansen, Gordon W. Semenoff, The D3-probe-D7 brane holographic fractional topological insulator, JHEP10 (2016) 079 (arXiv:1604.08548)