| dc.description |
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<sup>3</sup>. When q = e<sup>2πi/(N+K)</sup>, 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<sup>2πi/(N+K)</sup> and θ = 0 mod 2π/(N + K). |
