  Recently, we found the supersymmetric counterpart of the spectral triple.
When we restrict the representation space to the fermionic functions of matter
fields, the counterpart which we name "the triple" reduces to the original
spectral triple which defines noncommutative geometry. We see that the
fluctuation to the supersymmetric Dirac operator induced by algebra in the
triple generates vector supermultiplet which mediates gauge interaction.
Following the supersymmetric version of spectral action principle, we calculate
the heat kernel expansion of the square of fluctuated Dirac operator and obtain
the correct supersymmetric Yang-Mills action with U(N) gauge symmetry.
