Ludwik Dabrowski, Thomas Krajewski, Giovanni Landi
Some Properties of Non-linear $\sigma$-Models in Noncommutative Geometry
(51K, LaTex 2e)
ABSTRACT. 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.