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A Superconnection for Riemannian Gravity as Spontaneously Broken SL(4,R) Gauge Theory

Yuval Ne'eman
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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 ${\bar P}(4,R)$ (rank=3) in Kac' classification (even subgroup $\bar {SL}(4,R)$) prverline {SL}(4,R)$) provides for the most economical spontaneous breaking of $\bar{SL}(4,R)$ as gauge group, leaving just local $\bar{SO}(1,3)$ 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.

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Yuval Ne'eman. 1997-08-10. A Superconnection for Riemannian Gravity as Spontaneously Broken SL(4,R) Gauge Theory. https://doi.org/10.1016/s0370-2693(98)00326-8

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