Condensation Completion and Defects in 2+1D Topological Orders

Abstract: We review the condensation completion of a modular tensor category, which yields a fusion 2-category of codimension-1 and higher defects in a $2+1$D topological order. We apply the condensation completion to $2+1$D topological order with $\mathbb Z_2\times \mathbb Z_2$ and $\mathbb Z_4$ fusion rules. In these cases, we explicitly enumerate the $1$d and $0$d defects present in these topological orders, along with their fusion rules. We also talk about other applications of condensation completion: alternative interpretations of condensation completion of a braided fusion category; condensation completion of the category of symmetry charges and its correspondence to gapped phases with symmetry; for a topological order $\mathcal{C}$, one can also find all gapped boundaries of the stacking of $\mathcal{C}$ with its time-reversal conjugate through computing the condensation completion of $\mathcal{C}$.