Continuum field theory of three-dimensional topological orders with emergent fermions and braiding statistics

• DOI: 10.1103/physrevresearch.5.043111
• Publication Date: 2023-11-03T14:25:22Z
• Authors: Zhi-Feng Zhang; Qing-Rui Wang; Peng Ye
• Keywords: Topological algebra; Topological degeneracy; Topological ring

Universal topological data of topologically ordered phases can be captured by quantum field theory in continuous space time taking the limit low energies and long wavelengths. While previous continuum field-theoretical studies orders three-dimensional (3D) real focused on either self-statistics, braiding statistics, shrinking rules, fusion or dimensions, it has yet to systematically put all together a unified framework. Here, we construct $BF$ with twisted terms (e.g., $AAdA$ $AAB$) as well $K$-matrix $BB$ term simultaneously explore such reach anomaly-free orders. Following spirit famous Chern-Simons two-dimensional orders, present general formulas show how confines excitations, self-statistics particles is transmuted between bosonic one fermionic one. To explore, within framework, principle gauge invariance fundamentally influences possible realizations data. More concretely, actions (i) particle-loop braidings emergent fermions, (ii) multiloop (iii) Borromean rings calculate their universal Together efforts, our paper paves way toward more systematic complete analysis exotic properties 3D Several interesting future directions are also discussed.