# High electric charges in M-theory from quiver varieties

## TL;DR

This paper develops a geometric construction in M-theory that produces Calabi-Yau threefolds with matter fields carrying electric charges up to six, linking algebraic geometry with string theory compactifications.

## Contribution

It introduces a novel method to construct threefolds with matter of higher electric charges using families of ADE surfaces, extending previous models and relating to Morrison-Park geometry.

## Key findings

- Constructed threefolds with charges up to six.
- Established a relation between ADE surface families and electric charges.
- Provided a procedure applicable to F-theory models.

## Abstract

M-theory on a Calabi-Yau threefold admitting a small resolution gives rise to an Abelian vector multiplet and a charged hypermultiplet. We introduce into this picture a procedure to construct threefolds that naturally host matter with electric charges up to six. These are built as families of Du Val ADE surfaces (or ALE spaces), and the possible charges correspond to the Dynkin labels of the adjoint of the ADE algebra. In the case of charge two, we give a new derivation of the answer originally obtained by Curto and Morrison, and explicitly relate this construction to the Morrison-Park geometry. We also give a procedure for constructing higher-charge cases, which can often be applied to F-theory models.