Coupled wire model of symmetric Majorana surfaces of topological superconductors II: 32-fold periodic topological orders

We mimic the massless surface Majorana's of topological superconductors by coupled wire models in two spatial dimensions, and introduce many-body gapping interactions that preserve time reversal symmetry. Coupling with a $\mathbb{Z}_2$ gauge theory, the symmetric gapped surface generically carries a non-trivial $G_N$ topological order, where $N$ is the number of Majorana species and $G_N$ is some $SO(r)_1$ or $SO(3)_3$-like topological state. These form a 32-fold periodic class $G_N\cong G_{N+32}$, and a $\mathbb{Z}_{32}$ {\em relative} tensor product structure $G_{N_1}\otimes_bG_{N_2}\cong G_{N_1+N_2}$ by anyon condensation. We present the anyon structures of these topological states, and understand the topological orders through bulk-boundary correspondence and the Wilson structures on a torus geometry.