A SUPERCONNECTION FOR RIEMANNIAN GRAVITY AS SPONTANEOUSLY BROKEN SL(4,R) GAUGE-THEORY

A superconnection is a supermatrix whose even part contains the gauge- potential one-forms of a local gauge group, while the odd parts contai n the (0-form) Higgs fields. We demonstrate that the simple supergroup (P) over bar(4, R) (rank = 3) in Kac' classification (even subgroup < (SL)over bar>(4,R)) provides for the most economical spontaneous break ing of <(SL)over bar>(4,R) as gauge group, leaving just local <(SO)ove r bar>(1,3) unbroken. As a result, post-Riemannian SKY gravity is made to yield Einstein's theory as a low-energy (longer range) effective t heory. (C) 1998 Elsevier Science B.V. All rights reserved.