Noncommutative geometry, superconnections and Riemannian gravity as a low-energy theory

A superconnection is a supermatrix whose even part contains the gauge-potential one-forms of a local gauge group, while the odd parts contain the (zero-form) Higgs fields breaking the local symmetry spontaneously. The combined grading is thus odd everywhere and the superconnection can be directly derived from a formulation of Noncommutative Geometry, as the appropriate one-form in the relevant form calculus. The simple supergroup (P) over bar(4,R) (rank=3) in Kac' classification (even subgroup <(SL)over bar>(4,R)) provides the most economical spontaneous breaking of <(SL)over bar>(4,R) as gauge group leaving just local <(SO)over bar>(1,3) unbroken. Post-Riemannian SKY gravity thereby yields Einstein's theory as a low-energy (longer range) effective theory. The theory is renormalizable and may be unitary.