Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions

Understand

Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders.

• We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime ($5$D) in which \textit{topological excitations} include not only point-like \textit{particles}, but also two types of spatially extended objects: closed string-like \textit{loops} and two-dimensional closed \textit{membranes}.
• Especially, membranes have been rarely explored in the literature of topological orders.
• By introducing higher-form gauge fields, we construct exotic TQFT actions that include mixture of two distinct types of $BF$ topological terms and many twisted topological terms.