Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in $(3+1)$-Dimensions

Understand

Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions.

• In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of topological phases, e.g., quasi-particle braiding statistics, chiral central charge and even provides us a deep insight for the nature of topological phase transitions.
• Recently, topological phases of quantum matter are also intensively studied in $3+1$D and it has been shown that loop like excitation obeys the so-called three-loop-braiding statistics.
• In this paper, we will try to establish a TQFT framework to understand the quantum statistics of particle and loop like excitation in $3+1$D.