# $\text{SO}(N)_1$ Chern-Simons theory has no topological order?

According to appendix C5 in this paper, $\text{SO}(N)_1$ Chern-Simons theory has no topological order. On the other hand, in this paper, Prof. Wen showed $\text{SO}(5)_m$ CS theory has the ground state degeneracy (GSD) on torus $= (m+1)(m+2)/2$ and thus $\text{GSD}=3$ for $\text{SO}(5)_1$ theory. This computation is consistent with this post. I wonder how to resolve the contradiction. How do you compute GSD for $\text{SO}(N)_1$ CS theory to show $\text{GSD}=1$?

• Please consider spelling out abbreviations (GSD) and explaining what you mean by the subscript on the $\mathrm{SO}(N)$ to make this post more accessible. – ACuriousMind May 18 '17 at 10:38
• Minor comment to the post (v3): In the future please link to abstract pages rather than pdf files. – Qmechanic May 18 '17 at 19:22

Many field theories are not well defined. The $SO(N)_1$ CS theory in one paper may not be the same as the $SO(N)_1$ CS theory in another paper.
In my paper, the full theory is fermions coupled to $SO(5)$ gauge field. After integrating out the fermions, we get an effective $SO(5)_1$ CS theory. Its properties are given here https://www.math.ksu.edu/~gerald/voas/mtc/kmB2_1.html .