# Ground state degeneracy of non-Abelian topological phases from coupled wires

## TL;DR

This paper develops a coupled-wire method to construct and analyze non-Abelian topological phases, specifically focusing on the Moore-Read state, and discusses extensions to higher-dimensional phases.

## Contribution

It introduces a non-Abelian bosonization approach to realize and characterize non-Abelian topological orders from coupled wires, including their anyonic excitations and degeneracies.

## Key findings

- Constructed non-Abelian topological phases from coupled wires.
- Determined topological degeneracy and anyonic excitations of the phases.
- Extended the approach to potential three-dimensional non-Abelian phases.

## Abstract

We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic $su(2)^{\,}_{2}$ Moore-Read state, but the approach we outline here can be extended to general bosonic $su(2)^{\,}_{k}$ topological phases described by non-Abelian Chern-Simons theories. We also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.