Contents

# Contents

## Idea

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.

## Properties

### T-Duality with type I string theory

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):

### Duality with M-Theory

Under the duality between M-theory and type IIA string theory the O8-plane is identified with the M9-brane of Horava-Witten theory:

### Fractional branes at O-planes

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:

See also at intersecting D-brane models the section Intersection of D6s with O8s.

## References

Lift to M-theory: