nLab string network

Idea

There are $1/4$-BPS state solutions of type IIB supergravity which locally exhibit black branes in the shape of three $(p_i,q_i)$-strings jointly intersecting. Globally many of such 3-string junctions may combine to form a more complicated network of black string configurations, hence called a string network (Sen 97).

Properties

M-Theory lift to membrane triple junctions

The lift to 11d supergravity/M-theory of 3-string junctions is supposed to be given by membrane triple junctions.

Related concepts

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

The concept goes back to

• 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)

Relation to Lie algebras and Lie algebra representations:

• Oliver DeWolfe, Barton Zwiebach, String Junctions for Arbitrary Lie Algebra Representations, Nucl. Phys. B541 (1999) 509-565 (arXiv:hep-th/9804210)

• Oliver DeWolfe, Tamas Hauer, Amer Iqbal, Barton Zwiebach, Uncovering the Symmetries on $[p,q]$ 7-branes: Beyond the Kodaira Classification, Adv. Theor. Math. Phys. 3 (1999) 1785-1833 (arXiv:hep-th/9812028)

Relation to the D=6 N=(2,0) SCFT on M5-branes:

• Stefano Bolognesi, Kimyeong Lee, $1/4$ BPS String Junctions and N3 Problem in 6-dim $(2,0)$ Superconformal Theories, Phys. Rev. D.84. 126018 (arXiv:1105.5073)

See also

• Oleg Lunin, Brane webs and 1/4-BPS geometries, Journal of High Energy Physics, Volume 2008, JHEP09(2008) (arXiv:0802.0735)

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)