Noncommutative Geometry, Superconnections and Riemannian Gravity as a Low-Energy Theory

A superconnection is a supermatrix whose evenpart contains the gaugepotential one-forms of a localgauge group, while the odd parts contain the (zero-form)Higgs fields breaking the local symmetry spontaneously. The combined grading is thus odd everywhere andthe superconnection can be directly derived from aformulation of Noncommutative Geometry, as theappropriate one-form in the relevant form calculus. The simple supergroup (4, ) (rank = 3) in Kac' classification (evensubgroup (4,)) provides themost economical spontaneous breaking of (4,) as gauge group leaving just local (1,3) unbroken. Post-Riemannian SKY gravity thereby yields Einstein's theory asa low-energy (longer range) effective theory. The theoryis renormalizable and may be unitary.