I am currently trying to read through Garret Lisi's paper, An Exceptionally Simple Theory of Everything, and am having trouble understanding what it means for the gravitational fields to be described by a spin connection that is a Clifford bivector valued 1-form \begin{equation} \omega \in so(3,1) = Cl^2(3,1). \end{equation} I understand how the electroweak and strong are described by the special unitary group but I'm not sure what to make of gravity.(adsbygoogle = window.adsbygoogle || []).push({});

Additionally, how exactly does the frame defined by a Clifford vector valued 1-form \begin{equation}e \in Cl^1(3,1)\end{equation} combine with "a multiplet of Higgs scalar fields" in order to give fermions masses.

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# Clifford vector valued 1-form and gravity

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