A Superconnection for Riemannian Gravity as Spontaneously Broken SL(4,R) Gauge Theory
arXiv:hep-th/9708052 · doi:10.1016/S0370-2693(98)00326-8
Abstract
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 (0-form) Higgs fields; the combined grading is thus odd everywhere. We demonstrate that the simple supergroup (rank=3) in Kac' classification (even subgroup ) prverline {SL}(4,R)\bar{SL}(4,R)\bar{SO}(1,3)$ unbroken. As a result, post-Riemannian SKY gravity yields Einstein's theory as a low-energy (longer range) effective theory. The theory is renormalizable and may be unitary.
11 pages, latex