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

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

2007-03-08

arxiv.org/abs/hep-th/0703089v2

JHEP 0706:023,2007

Physics

High Energy Physics

High Energy Physics - Theory

19 pages; v2: minor typo corrected, 1 paragraph added, published version

Scientific paper

10.1088/1126-6708/2007/06/023

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).

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