In theoretical physics orientifold is a generalization of the notion of orbifold, proposed by Augusto Sagnotti in 1987. The novelty is that in the case of string theory the non-trivial element(s) of the orbifold group includes the reversal of the orientation of the string. Orientifolding therefore produces unoriented strings—strings that carry no "arrow" and whose two opposite orientations are equivalent. Type I string theory is the simplest example of such a theory and can be obtained by orientifolding type IIB string theory.
Contents
In mathematical terms, given a smooth manifold
Application to string theory
In string theory
Supersymmetry breaking
The six dimensions take the form of a Calabi-Yau for reasons of partially breaking the supersymmetry of the string theory to make it more phenomenologically viable. The Type II string theories have 32 real supercharges, and compactifying on a six-dimensional torus leaves them all unbroken. Compactifying on a more general Calabi-Yau sixfold, 3/4 of the supersymmetry is removed to yield a four-dimensional theory with 8 real supercharges (N=2). To break this further to the only non-trivial phenomenologically viable supersymmetry, N=1, half of the supersymmetry generators must be projected out and this is achieved by applying the orientifold projection.
Effect on field content
A simpler alternative to using Calabi-Yaus to break to N=2 is to use an orbifold originally formed from a torus. In such cases it is simpler to examine the symmetry group associated to the space as the group is given in the definition of the space.
The orbifold group
The locus where the orientifold action reduces to the change of the string orientation is called the orientifold plane. The involution leaves the large dimensions of space-time unaffected and so orientifolds can have O-planes of at least dimension 3. In the case of
More generally, one can consider orientifold Op-planes where the dimension p is counted in analogy with Dp-branes. O-planes and D-branes can be used within the same construction and generally carry opposite tension to one another.
However, unlike D-branes, O-planes are not dynamical. They are defined entirely by the action of the involution, not by string boundary conditions as D-branes are. Both O-planes and D-branes must be taken into account when computing tadpole constraints.
The involution also acts on the complex structure (1,1)-form J
This has the result that the number of moduli parameterising the space is reduced. Since