Induced QCD from the Noncommutative Geometry of a Supermanifold

Details Induced QCD from the Noncommutative Geometry of a Supermanifold Induced QCD from the Noncommutative Geometry of a Supermanifold

1994-11-10

arxiv.org/abs/hep-th/9411075v2

J.Math.Phys. 36 (1995) 2727-2740

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, latex

Scientific paper

10.1063/1.531062

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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