The simplest toroidally compactified string theories exhibit a duality between small and large radii: compactification on a circle, for example, is invariant under R → 1/(2R). Compactification on more general Lorentzian lattices (e.g. toroidal compactification in the presence of background metric, antisymmetric tensor, and gauge fields) yields theories for which a large-small equivalence is not...

Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space R/Γ as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group Γ on Euclidean space Rd and a projective representation U of Γ. The choice of Hilbert space on ...