Defects in the 3-dimensional toric code model form a braided fusion 2-category

A bstract It was well known that there are e -particles and m -strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ 2 topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ 2 topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.