  We derive supersymmetric quantum chromodynamics from a noncommutative
manifold, using the spectral action principle of Chamseddine and Connes. After
a review of the Einstein-Yang-Mills system in noncommutative geometry, we
establish in full detail that it possesses supersymmetry. This noncommutative
model is then extended to give a theory of quarks, squarks, gluons and gluinos
by constructing a suitable noncommutative spin manifold (i.e. a spectral
triple). The particles are found at their natural place in a spectral triple:
the quarks and gluinos as fermions in the Hilbert space, the gluons and squarks
as bosons as the inner fluctuations of a (generalized) Dirac operator by the
algebra of matrix-valued functions on a manifold. The spectral action principle
applied to this spectral triple gives the Lagrangian of supersymmetric QCD,
including soft supersymmetry breaking mass terms for the squarks. We find that
these results are in good agreement with the physics literature.
