Some Properties of Non-linear $σ$-Models in Noncommutative Geometry

Physics – High Energy Physics – High Energy Physics - Theory

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15 pages, latex. Talk presented at the Euroconference ``Hopf algebras and noncommutative geometry in field theory and particle

Scientific paper

10.1142/S0217979200001898

We introduce non-linear $\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some characteristic features of the corresponding $\sigma$-models. In particular we construct a $\sigma$-model instanton with topological charge equal to 1. We also define and investigate some properties of a noncommutative analogue of the Wess-Zumino-Witten model.

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