#### Title

Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory

#### Document Type

Article

#### Publication Date

6-1-2007

#### Abstract

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 ≤ e2πi/(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 ≤ e2πi/(N+K) and θ ≤ 0 mod 2π/(N + K). © SISSA 2007.

#### Recommended Citation

Naculich, Stephen G. and Schnitzer, Howard J., "Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory" (2007). *Physics Faculty Publications*. 129.

https://digitalcommons.bowdoin.edu/physics-faculty-publications/129