Twelve-dimensional aspects of four-dimensional N = 1 type I vacua

Four-dimensional supergravity theories are reinterpreted in a 12-dimensional F-theory framework. The O(8) symmetry of N = 8 supergravity is related to a reduction of F-theory on T8, with the seventy scalars formally associated, by O(8) triality, to a fully compactified four-form A4. For the N = 1 type I model recently obtained from the type IIB string on the Z orbifold, we identify the Kähler manifold of the untwisted scalars in the unoriented closed sector with the generalized Siegel upper-half plane Sp(8, R)(SU(4) × U(1)). The SU(4) factor reflects the holonomy group of Calabi-Yau four-folds.