Orientifold Limit of F-theory Vacua

TL;DR

This paper explores how F-theory compactifications can be approximated by orientifold limits of type IIB string theory, especially focusing on Calabi-Yau three-folds and the conditions under which singularities are preserved.

Contribution

It provides a formal reduction of F-theory on Calabi-Yau (n+1)-folds to orientifolds of type IIB theory, highlighting the role of singularities in this correspondence.

Findings

F-theory on elliptically fibered Calabi-Yau 3-folds can be approximated by type IIB orientifolds.

The auxiliary n-fold may be singular if the original (n+1)-fold is singular.

The analysis is exemplified using F-theory on Calabi-Yau 3-folds over base $F_n$.

Abstract

We show how an F-theory compactified on a Calabi-Yau (n+1)-fold in appropriate weak coupling limit reduces formally to an orientifold of type IIB theory compactified on an auxiliary complex n-fold. In some cases (but not always) if the original (n+1)-fold is singular, then the auxiliary n-fold is also singular. We illustrate this by analysing F-theory on elliptically fibered Calabi-Yau 3-folds on base $F_n$.