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

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

2000-03-13

arxiv.org/abs/hep-th/0003099v2

Int.J.Mod.Phys. B14 (2000) 2367-2382

Physics

High Energy Physics

High Energy Physics - Theory

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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