Induced QCD from the Noncommutative Geometry of a Supermanifold

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.

15 pages, latex

References in corpus (5)

• Gravity in Non-Commutative Geometry
• Induced QCD at Large N
• Grand Unification in Non-Commutative Geometry
• Connection between Space-Time Supersymmetry and Non-Commutative Geometry
• The Chern-Simons Action in Non-Commutative Geometry