nLab brane intersection

Idea

intersection of branes in string theory

Examples

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

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

More:

M5-brane with KK-monopole:

$$(5\vert M5, KK) = \left\{ \array{ x_0 & - & - & - & - & x_5 & x_6 & x_7 & x_8 & x_9 & - \\ x_0 & A_1 & A_2 & A_3 & z & x_5 & x_6 & x_7 & x_8 & x_9 & x_{10} } \right.$$

(BREJS 97 (14))

For more see at Half NS5-branes

D4-branes ending on D6-branes from M5-branes in MK6-branes:

Hashimoto 98, see also Smith 02 (245)

Related concepts

• wrapped brane

• polarized brane

• color branes and flavor branes

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

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

General

• Douglas J. Smith, Intersecting brane solutions in string and M-theory, Class.Quant.Grav.20:R233, 2003 (arXiv:hep-th/0210157)

• Akikazu Hashimoto, Supergravity Solutions for Localized Intersections of Branes, JHEP 9901 (1999) 018 (arXiv:hep-th/9812159)

For M-branes:

• Eric Bergshoeff, M. Roo, E. Eyras, Bert Janssen, J. P. Schaar, Intersections involving waves and monopoles in eleven dimensions, Class. Quantum Grav. 14 2757 (arXiv:hep-th/9704120, publisher)

• Eric Bergshoeff, Joaquim Gomis, Paul Townsend, M-brane intersections from worldvolume superalgebras, Phys.Lett. B421 (1998) 109-118 (arXiv:hep-th/9711043)

• Paul Townsend, section 4 of M-theory from its superalgebra (arXiv:hep-th/9712004)

• Sergey A. Cherkis, Supergravity Solution for M5-brane Intersection (arXiv:hep-th/9906203)

Brane webs

Intersections of branes of equal dimension may form regular patterns known as brane webs. This applies notably in type IIB string theory where (p,q)-strings may form “string webs” (references below) and (p,q)5-branes may form “5-brane webs” (references further below)

General

• Oleg Lunin, Brane webs and 1/4-BPS geometries, JHEP09 (2008) (arXiv:0802.0735)

String webs

• Ashoke Sen, String Network, JHEP 9803:005, 1998 (arXiv:hep-th/9711130)

• Soo-Jong Rey, Jung-Tay Yee, BPS Dynamics of Triple $(p,q)$ String Junction, Nucl.Phys. B526 (1998) 229-240 (arXiv:hep-th/9711202)

• Keshav Dasgupta, Sunil Mukhi, BPS Nature of 3-String Junctions, Phys.Lett. B423 (1998) 261-264 (arXiv:hep-th/9711094)

Via tropical geometry:

• Koushik Ray, String networks as tropical curves, JHEP 0809:098, 2008 (arXiv:0804.1870)

The lift to 11d supergravity/M-theory via membrane triple junctions is discussed in

• Morten Krogh, Sangmin Lee, String Network from M-theory, Nucl. Phys. B516:241-254, 1998 (arXiv:hep-th/9712050)

• P. Ramadevi, Supergravity Solution for Three-String Junction in M-Theory, JHEP 0006 (2000) 005 (arXiv:hep-th/9906247)

5-brane webs

• Ofer Aharony, Amihay Hanany, section 3 of Branes, Superpotentials and Superconformal Fixed Points, Nucl.Phys.B504:239-271, 1997 (arXiv:hep-th/9704170)

• Barak Kol, 5d Field Theories and M Theory, JHEP 9911 (1999) 026 (arXiv:hep-th/9705031)

• Ofer Aharony, Amihay Hanany, Barak Kol, Webs of $(p,q)$ 5-branes, Five Dimensional Field Theories and Grid Diagrams, JHEP 9801:002,1998 (arXiv:hep-th/9710116)

• Francesco Benini, Sergio Benvenuti, Yuji Tachikawa, Webs of five-branes and $N=2$ superconformal field theories, JHEP 0909:052,2009 (arXiv:0906.0359)

• Sung-Soo Kim, Masato Taki, Futoshi Yagi, Tao Probing the End of the World, Prog. Theor. Exp. Phys. 2015, 083B02 (arXiv:1504.03672)

• Brice Bastian, Stefan Hohenegger, Five-Brane Webs and Highest Weight Representations (arXiv:1706.08750)

• Justin Kaidi, $(p,q)$-strings probing five-brane webs, J. High Energ. Phys. (2017) 2017: 87 (arXiv:1708.03404)

• Michael Gutperle, Andrea Trivella, Christoph F. Uhlemann, Type IIB 7-branes in warped $AdS_6$: partition functions, brane webs and probe limit, JHEP04(2018)135 (arXiv:1802.07274)

• Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi, Dualities and 5-brane webs for 5d rank 2 SCFTs (arXiv:1806.10569)