In type II string theory on orientifolds, one says O-plane for the fixed point locus of the $\mathbb{Z}_2$-involution (see at real space).
O-planes carry D-brane charges in KR-theory (Witten 98), see (DMR 13) for a mathematical account. They serve RR-field tadpole cancellation and as such play a key role in the construction of intersecting D-brane models for string phenomenology.
Under T-duality type I string theory is dual to type II string theory with orientifold planes (reviewed e.g. in Ibanez-Uranga 12, section 5.3.2):
Under the duality between M-theory and type IIA string theory the O8-plane is identified with the M9-brane of Horava-Witten theory:
from GKSTY 02, section 3
By the discussion at D-branes ending on NS5 branes, a black D6-brane may end on a black NS5-brane, and in fact a priori each brane NS5-brane has to be the junction of two black D6-branes.
from GKSTY 02
If in addition the 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:
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
See also at intersecting D-brane models the section Intersection of D6s with O8s.
Luis Ibáñez, Angel Uranga, section 5.3.2 of String Theory and Particle Physics – An Introduction to String Phenomenology, Cambridge 2012
Edward Witten, section 5 of D-branes and K-theory, J. High Energy Phys., 1998(12):019, 1998 (arXiv:hep-th/9810188)
Charles Doran, Stefan Mendez-Diez, Jonathan Rosenberg, T-duality For Orientifolds and Twisted KR-theory (arXiv:1306.1779)
Lift to M-theory:
Eric G. Gimon, On the M-theory Interpretation of Orientifold Planes (arXiv:hep-th/9806226)
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)
Amihay Hanany, Barak Kol, section 3 of On Orientifolds, Discrete Torsion, Branes and M Theory, JHEP 0006 (2000) 013 (arXiv:hep-th/0003025)
Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi, 6d SCFTs, 5d Dualities and Tao Web Diagrams (arXiv:1509.03300)
See also
Last revised on December 11, 2018 at 01:27:11. See the history of this page for a list of all contributions to it.