nLab M5-MO9 brane bound state

Idea

The brane intersection of M5-branes with MO9-planes – the “half M5-brane”.

Equivalently:

• under duality between M-theory and heterotic string theory: black NS5-brane solitons in heterotic string theory.

• under duality between M-theory and type IIA string theory:

  D4-D8-brane bound states or half NS5-brane in type I' string theory

graphics grabbed from HSS18, Example 2.2.7

graphics grabbed from SS 19, Section 4

In string theory

As Yang-Mills instantons in heterotic string theory

In (dual) heterotic string theory wrapped NS5-branes are equivalently Yang-Mills instantons in the transversal Yang-Mills theory (Strominger 90, Witten 96, p. 10) – as is generally the case for Dp-D(p+4)-brane bound states (see there).

As half NS5-branes in type I’

(For more see at half NS5-brane.)

If a black NS5-brane sits at an O8-plane, hence at the orientifold fixed point-locus, then in the ordinary $\mathbb{Z}/2$-quotient it appears as a “half-brane” with only one copy of D6-branes ending on it:

from GKSTY 02

(In Hanany-Zaffaroni 99 this is interpreted in terms of the 't Hooft-Polyakov monopole.)

The lift to M-theory of this situation is an M5-brane intersecting an M9-brane (see at MO5-plane and at heterotic M-theory on ADE-orbifolds):

from GKSTY 02

Alternatively the O8-plane may intersect the black D6-branes away from the black NS5-brane:

from HKLY 15

In general, some of the NS5 sit away from the O8-plane, while some sit on top of it:

from Hanany-Zaffaroni 98

graphics grabbed from Apruzzi-Fazzi 17, p. 18

Related concepts

• heterotic M-theory on ADE-orbifolds

• E-string

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 heterotic Yang-Mills instantons

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)

As half M5-branes

• Fabio Apruzzi, Marco Fazzi, Section 2.1.2 of: AdS7/CFT6 with orientifolds, JHEP 01 (2018) 124 (arXiv:1712.03235)

• 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)