Topological Orders in (4+1)-Dimensions

TL;DR

This paper explores the structure of (4+1)-dimensional topological orders, showing super topological orders are Morita trivial with gapped boundaries, while bosonic ones are infinitely diverse and Morita inequivalent.

Contribution

It proves all super (4+1)-dimensional topological orders are Morita trivial with gapped boundaries, contrasting with the infinite variety of bosonic orders.

Findings

Super (4+1)-dimensional topological orders are Morita trivial.

All super (4+1)-dimensional topological orders admit gapped boundaries.

There are infinitely many Morita-inequivalent bosonic (4+1)-dimensional topological orders.

Abstract

We investigate the Morita equivalences of (4+1)-dimensional topological orders. We show that any (4+1)-dimensional super (fermionic) topological order admits a gapped boundary condition -- in other words, all (4+1)-dimensional super topological orders are Morita trivial. As a result, there are no inherently gapless super (3+1)-dimensional theories. On the other hand, we show that there are infinitely many algebraically Morita-inequivalent bosonic (4+1)-dimensional topological orders.