Local Calabi-Yau 3-folds for some rank 2 shrinkable surfaces

TL;DR

The paper constructs specific local Calabi-Yau 3-folds containing rank 2 shrinkable surfaces, motivated by 5d SCFTs, generalizing previous local surface constructions.

Contribution

It introduces a new construction of non-compact Calabi-Yau 3-folds with rank 2 shrinkable surfaces, extending prior methods for smooth surfaces.

Findings

Construction of a smooth, non-compact Calabi-Yau 3-fold with a rank 2 shrinkable surface

Generalization of local surface construction techniques

Potential applications to 5d superconformal field theories

Abstract

Motivated by 5d rank 2 SCFTs, we construct a smooth, non-compact Calabi-Yau 3-fold $X$ containing a rank 2 shrinkable surface $S=S_1\cup S_2$ glued over a smooth curve. This construction will be a generalization of the construction of a local surface for a smooth surface $S$