 00224 Ludwik Dabrowski, Thomas Krajewski, Giovanni Landi
 Some Properties of Nonlinear $\sigma$Models in Noncommutative Geometry
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May 15, 00

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Abstract. We introduce nonlinear $\sigma$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 WessZuminoWitten model.
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