orientifold

An orientifold is a type of string theory construction obtained by gauging a symmetry that includes worldsheet orientation reversal. In Type II theories, one mods out by Omega times a spacetime involution, such as a reflection, yielding a theory with unoriented (non-orientable) worldsheet topology. The fixed loci of the geometric action are called orientifold planes, labeled O_p, which extend in p spatial dimensions. O-planes carry a negative Ramond-Ramond (RR) charge and tension and act as sources for RR fields.

The orientifold projection removes some states from the spectrum and introduces unoriented strings. To build consistent vacua, the total RR charge must cancel, typically by adding D-branes and/or fluxes; tadpole cancellation conditions constrain the allowed configurations. A well-known example is the Type I string, which can be obtained as the orientifold of Type IIB by worldsheet parity Omega with an O9-plane and 32 D9-branes, yielding the SO(32) gauge theory.

Variants of orientifolds differ by the choice of the geometric involution and discrete choices, producing O_p-planes with different charges (and sometimes multiple variants for a given p, e.g., O3^− and O3^+ in certain setups). Orientifolds are used to realize lower-dimensional gauge theories, break supersymmetry, and construct phenomenological models. They are related by dualities to other string constructions, including intersecting-brane models, and play a central role in compactifications with fluxes and moduli stabilization.