nLab M9-brane




The 2\mathbb{Z}_2-orbifold/higher orientifold fixed point in Hořava-Witten theory might be called it O9-plane but is often called the M9-brane (e.g. GKSTY 02, section 3, Moore-Peradze-Saulina 04), even though it is on a different conceptual footing than the genuine M2-brane and M5-brane.

In (Hull 97, pages 8-9) the M9-brane was argued to be the object whose charge is the Poincaré dual to the time-component of the M2-brane charge as it appears in the M-theory super Lie algebra via

2( 10,1) * 2( 10) * 9 10. \wedge^2 (\mathbb{R}^{10,1})^\ast \simeq \wedge^2 (\mathbb{R}^{10})^\ast \oplus \wedge^{9} \mathbb{R}^{10} \,.

(In the same way the time component of the M5-brane charge is argued to be dual to the charge of the KK-monopole, see there.)

Under the duality between M-theory and type IIA string theory the M9-brane may be identified with the O8-plane:

from GKSTY 02, section 3

This may be used to understand the gauge enhancement to E8-gauge groups at the heterotic boundary of Horava-Witten theory:


from GKSTY 02, section 3

Table of branes appearing in supergravity/string theory (for classification see at brane scan).

branein supergravitycharged under gauge fieldhas worldvolume theory
black branesupergravityhigher gauge fieldSCFT
D-branetype IIRR-fieldsuper Yang-Mills theory
(D=2n)(D = 2n)type IIA\,\,
D0-brane\,\,BFSS matrix model
D4-brane\,\,D=5 super Yang-Mills theory with Khovanov homology observables
D6-brane\,\,D=7 super Yang-Mills theory
(D=2n+1)(D = 2n+1)type IIB\,\,
D1-brane\,\,2d CFT with BH entropy
D3-brane\,\,N=4 D=4 super Yang-Mills theory
(D25-brane)(bosonic string theory)
NS-branetype I, II, heteroticcircle n-connection\,
string\,B2-field2d SCFT
NS5-brane\,B6-fieldlittle string theory
D-brane for topological string\,
M-brane11D SuGra/M-theorycircle n-connection\,
M2-brane\,C3-fieldABJM theory, BLG model
M5-brane\,C6-field6d (2,0)-superconformal QFT
M9-brane/O9-planeheterotic string theory
topological M2-branetopological M-theoryC3-field on G2-manifold
topological M5-brane\,C6-field on G2-manifold
membrane instanton
M5-brane instanton
D3-brane instanton
solitons on M5-brane6d (2,0)-superconformal QFT
self-dual stringself-dual B-field
3-brane in 6d


Early discussion of the possibility of a kind of 9-brane in 11d supergravity:

On M9-branes (and apparently introducing that terminology) as lifts of the D8-branes in massive type IIA string theory:

Further discussion:

  • M. P. Garcia del Moral, P. Leon, A. Restuccia, Wordsheet description of a massive type IIA superstring in 10D [arXiv:2306.16620]

A proposal for a description of the M9 as an higher WZW theory is in

  • Takeshi Sato, A 10-form Gauge Potential and an M-9-brane Wess-Zumino Action in Massive 11D Theory, Phys. Lett. B477 (2000) 457-468 (arXiv:hep-th/9912030)

Discussion of how the M2-brane and the M5-brane may arise from this by tachyon condensation is in

Discussion of the M9 as the dual in Horava-Witten theory of O8-planes in type II string theory is in

  • E. Gorbatov, V.S. Kaplunovsky, J. Sonnenschein, Stefan Theisen, S. Yankielowicz, section 3 of On Heterotic Orbifolds, M Theory and Type I’ Brane Engineering, JHEP 0205:015, 2002 (arXiv:hep-th/0108135)

see also at Intersection of D6s with O8s

Cohomological discussion of ninebrane structures is in

See also

Discussion of open M5-branes ending on the M9-brane is in

Discussion as exotic branes in exceptional field theory:

p. 109: “conjectured M9-brane which should more properly be called M8-brane.”

Last revised on July 2, 2023 at 09:46:50. See the history of this page for a list of all contributions to it.