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arXiv · hep-th/0703089

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

Stephen G. Naculich·Howard J. Schnitzer
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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 = 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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Stephen G. Naculich, Howard J. Schnitzer. 2007-06-11. Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory. https://doi.org/10.1088/1126-6708%2F2007%2F06%2F023

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