Two-dimensional topological order and operator algebras

TL;DR

This paper reviews the mathematical connections between two-dimensional topological order, operator algebras, and tensor categories, highlighting recent advances in understanding anyon condensation, domain walls, and conformal field theory.

Contribution

It synthesizes recent developments linking topological order with operator algebra theory, emphasizing the role of tensor categories and conformal field theory connections.

Findings

Operator algebras provide a framework for understanding topological order.

Tensor categories are central to describing anyon condensation and domain walls.

Connections to conformal field theory deepen the mathematical understanding of topological phases.

Abstract

We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to 2-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras.