Supersymmetric QCD in the Noncommutative Geometry
  Introduction of supersymmetry into the noncommutative geometry is investigated. We propose a new Dirac operator which plays the role of the metric over the extended algebra of chiral and antichiral supermultiplets and is invariant under the supersymmetry transformations. Inner automorphisms for the algebra generate vector supermultiplets as an internal fluctuation of the metric. We show that the supersymmetric QCD action for these supermultiplets is correctly given by the spectral action principle. 
Satoshi Ishihara, Hironobu Kataoka, Atsuko Matsukawa, Hikaru Sato and   Masafumi Shimojo
hep-th