Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d
  qYM theory   We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N).
The U(N) WZW model is only well-defined for odd level K, and this model is
shown to exhibit level-rank duality in a much simpler form than that for SU(N).
The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality,
distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When
q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be
expressed as a sum over a finite subset of U(N) representations. When N and K
are odd, the qYM theory exhibits N <--> K duality, provided q = e^{2 pi
i/(N+K)} and theta = 0 mod 2 pi /(N+K).

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess