Anyon and Loop Braiding Statistics in Field Theories with a Topological $\hat{I}˜-$term

Abstract

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 $\hat{I}˜$-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 $\hat{I}˜$-term.

4 pages, 3 figures