# Compactifying fracton stabilizer models

## TL;DR

This paper explores how three-dimensional fracton stabilizer models, specifically the X-cube model and Haah's cubic code, behave when compactified to two dimensions, revealing new topological phases and symmetry-enriched phenomena.

## Contribution

It introduces the study of 2D topological phases resulting from compactifying 3D fracton models and uncovers translation symmetry-enrichment effects in the cubic code.

## Key findings

- Identification of 2D topological phases as a function of compactification radius
- Discovery of translation symmetry-enrichment in the cubic code
- Observation of twisted boundary conditions in the compactified models

## Abstract

We investigate two dimensional compactifications of three dimensional fractonic stabilizer models. We find the two dimensional topological phases produced as a function of compactification radius for the X-cube model and Haah's cubic code. Furthermore, we uncover translation symmetry-enrichment in the compactified cubic code that leads to twisted boundary conditions.