Composing topological domain walls and anyon mobility

TL;DR

This paper develops a 3-categorical framework to decompose stacks of topological domain walls into fundamental sectors, linking superselection sectors to anyon mobility and extending understanding to anomalous topological orders.

Contribution

It introduces a novel 3-category approach to decompose topological domain walls into indecomposable sectors, incorporating anomalies and anyon mobility.

Findings

Framework for decomposing multiple domain walls into superselection sectors

Characterization of sectors via domain wall particle mobility

Extension of previous models to anomalous topological orders

Abstract

Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a framework for decomposing stacks of multiple domain walls into superselection sectors - i.e., into fundamental domain wall types that cannot be mixed by any local operators. Such a decomposition can be understood using an alternate framework in the case that the topological order is anomaly-free, in the sense that it can be realized by a commuting projector lattice model. By placing these Witt equivalences in the context of a 3-category of potentially anomalous (2+1)D topological orders, we develop a framework for computing the decomposition of parallel topological domain walls into indecomposable superselection sectors, extending the previous understanding to topological orders with non-trivial anomaly. We characterize the superselection sectors in terms of domain wall particle mobility, which we formalize in terms of tunnelling operators. The mathematical model for the 3-category of topological orders is the 3-category of fusion categories enriched over a fixed unitary modular tensor category.