6
$\begingroup$

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 $\text{GSD}=1$?

$\endgroup$
  • 1
    $\begingroup$ 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. $\endgroup$ – ACuriousMind May 18 '17 at 10:38
  • 1
    $\begingroup$ Minor comment to the post (v3): In the future please link to abstract pages rather than pdf files. $\endgroup$ – Qmechanic May 18 '17 at 19:22
2
$\begingroup$

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 .

$\endgroup$
  • $\begingroup$ Thank you, Prof. Wen. I am confused about the gauge group of (69) in your paper, where the gauge group is generated by sp4 Lie algebra. At the algebra level, sp4~so(5) but at the group level, SO(5) is not simply connected while Sp4 is. I wonder why the resulting theory after integrating the fermions is SO(5) CS theory instead of Sp4 CS theory. $\endgroup$ – Charles Jun 5 '17 at 20:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.