Anyon and Loop Braiding Statistics in Field Theories with a Topological   $\Theta-$term
  We demonstrate that the anyon statistics and three-loop statistics of various 2d and 3d topological phases can be derived using semiclassical nonlinear Sigma model field theories with a topological $\Theta$-term. In our formalism, the braiding statistics has a natural geometric meaning: The braiding process of anyons or loops leads to a nontrivial field configuration in the space-time, which will contribute a braiding phase factor due to the $\Theta$-term. 
Zhen Bi, Yi-Zhuang You, Cenke Xu
cond-mat.str-el