Gauged Noncommutative Wess-Zumino-Witten Models

We investigate the Kac-Moody algebra of noncommutative Wess-Zumino-Witten model and find its structure to be the same as the commutative case. Various kinds of gauged noncommutative WZW models are constructed. In particular, noncommutative $U(2)\mathrm{/}U(1)$ WZW model is studied and by integrating out the gauge fields, we obtain a noncommutative non-linear $\sigma$-model.