# Orientifold limits of singular $F$-theory vacua

## TL;DR

This paper constructs orientifold limits for singular F-theory vacua with various gauge groups, demonstrating that the universal tadpole relation involves stringy Chern classes rather than classical ones.

## Contribution

It introduces a method to find orientifold limits of singular F-theory vacua and shows the universal tadpole relation involves stringy Chern classes for these cases.

## Key findings

- Universal tadpole relations are satisfied for all constructed limits.
- Stringy Chern classes replace classical ones in tadpole contributions for singular cases.
- Homological identities encode D3 charge matching in these limits.

## Abstract

We construct global orientifold limits of singular $F$-theory vacua whose associated gauge groups are SO(3), SO(5), SO(6), $F_4$, SU(4), and Spin(7). For each limit we show a universal tadpole relation is satisfied, which is a homological identity whose dimension-zero component encodes the matching of the D3 charge between each $F$-theory compactification and its orientifold limit. While for smooth $F$-theory compactifications which admit global orientifold limits the contribution to the associated universal tadpole relation comes from its Chern class, we show that for all singular $F$-theory compactifications under consideration, the contribution to the universal tadpole relation comes from its \emph{stringy} Chern class.