Twelve-Dimensional Aspects of Four-Dimensional N=1 Type I Vacua

TL;DR

This paper reinterprets four-dimensional N=1 type I string vacua within a 12-dimensional F-theory framework, linking supergravity symmetries to higher-dimensional geometric structures and identifying scalar moduli spaces with generalized Siegel upper-half planes.

Contribution

It introduces a 12-dimensional perspective on N=1 type I vacua, connecting supergravity scalars to F-theory compactifications and geometric moduli spaces.

Findings

Reinterpretation of N=1 vacua in 12D F-theory framework

Identification of scalar moduli space with Siegel upper-half plane

Relation of symmetry groups to Calabi-Yau fourfold holonomy

Abstract

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 T_8, with the seventy scalars formally associated, by O(8) triality, to a fully compactified four-form A_4. For the N=1 type I model recently obtained from the type IIB string on the Z orbifold, we identify the K\"ahler manifold of the untwisted scalars in the unoriented closed sector with the generalized Siegel upper-half plane Sp(8,R)/(SU(4) \times U(1)). The SU(4) factor reflects the holonomy group of Calabi-Yau fourfolds.