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arXiv · hep-th/9411075

Induced QCD from the Noncommutative Geometry of a Supermanifold

Jussi Kalkkinen
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Abstract

We study the noncommutative geometry of a two-leaf Parisi--Sourlas supermanifold in Connes' formalism using different $K$-cycles over the Grassmann algebra valued functions on the supermanifold. We find that the curvature of the trivial noncommutative vector bundle defines in the simplest case the super Yang--Mills action coupled to a scalar field. By considering a modified Dirac operator and a suitable limit of its parameters we then obtain an action that turns out to be the continuum limit of the induced QCD in Kazakov--Migdal model.

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Jussi Kalkkinen. 1994-11-10. Induced QCD from the Noncommutative Geometry of a Supermanifold. https://doi.org/10.1063/1.531062

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