Discrete moduli for type I compactifications

Abstract

We study type I compactification on a 4-torus, with a nontrivial discrete background RR 4-form field. By using string dualities and recent insights for gauge theories on tori, we find that a nontrivial background for the RR 4-form is correlated with $\mathrm{Spin}(32)/{Z}_{2}$ bundles that are described by a ``nontrivial quadruple'' of holonomies. We also briefly discuss other discrete moduli for the type I string, and variants of orientifold planes.