Timeline for Topological ground state degeneracy of SU(N), SO(N), Sp(N) Chern-Simons theory
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S May 4, 2014 at 16:35 | history | edited | Danu | CC BY-SA 3.0 |
some typo: is may -> may, Fucks to Fuchs, #(...) counts the volume.
|
| May 4, 2014 at 16:26 | review | Suggested edits | |||
| S May 4, 2014 at 16:35 | |||||
| Mar 8, 2014 at 22:15 | vote | accept | wonderich | ||
| Jan 10, 2014 at 20:51 | comment | added | wonderich | @ DavidBarMoshe (or Trimok), it will be really nice if you can shed light on the relation between C-S theory's GSD and the Cartan matrix of a given gauge group. Please. | |
| Jan 9, 2014 at 19:09 | comment | added | Trimok | @DavidBarMoshe : I am certainly wrong, but it seems to me that your formula $0 \leq \sum_{i=1}^r \frac{2 \lambda. \alpha^{(i)}}{ \alpha^{(i)}. \alpha^{(i)}}\leq k$, for instance in a rank $2$ algebra, always give the constraint $0\leq n_1 + n_2 \leq k$, while I have the feeling that it is not correct for $G_2$ (well, I based my (maybe false) intuition) on the formula $1.7$ of this paper. | |
| Jan 9, 2014 at 17:36 | comment | added | David Bar Moshe | @Idear For the case of $SO(N)$ You can use equation (1b) together with the coefficients given in sections 3.B and 3.D of Gannon's article arxiv.org/abs/hep-th/0106123 to compute the integrable highest weights. I'll correct and update my answer soon. I used the symbol # for the cardinality of the set. Yes, the rank is the dimension of the Cartan matrix, it is also the dimension of the maximal torus $T$. | |
| Jan 8, 2014 at 20:33 | comment | added | wonderich | @David, By saying "leading exponent is 2 which is the rank of SU(3)" I know exponent is 2, but you mean "the rank of SU(3) is 2" is for Cartan matrix (correct ?) | |
| Jan 8, 2014 at 20:27 | comment | added | wonderich | @ David, if there are explicit formulas for g=1 T2 torus of SO(N) level-k Chern-Simons theory is just good enough. (in any Ref) Trimok's ref seems to provide SU(N), Sp(N) already. | |
| Jan 8, 2014 at 19:26 | comment | added | wonderich | @ David, now I understand your Eq.(4), you are saying: $$GSD=\#(n1≥0,n2≥0,0≤n1+n2≤k)=(k+1)(k+2)/2$$; i.e. counting the volume. Perhaps adding a bracket is more clear. | |
| Jan 8, 2014 at 18:30 | history | edited | Trimok | CC BY-SA 3.0 |
Correction Link
|
| Jan 8, 2014 at 17:33 | comment | added | wonderich | Dear David, +1, you are certainly an expert in the field. Thank you so much, let me take a further look, hopefully get back to you soon. | |
| Jan 8, 2014 at 15:25 | history | edited | David Bar Moshe | CC BY-SA 3.0 |
added 12 characters in body
|
| Jan 8, 2014 at 15:09 | history | answered | David Bar Moshe | CC BY-SA 3.0 |