TL;DR
This paper develops a gauge theory of super SL(2,C), proposing a quadratic action based on the curvature of the super gauge connection, leading to a natural metric after symmetry breaking.
Contribution
It introduces a novel super SL(2,C) gauge theory framework with a MacDowell-Mansouri type action for gravity.
Findings
Defines a super SL(2,C) gauge connection and curvature.
Proposes a quadratic gauge action dependent on curvature.
Achieves a natural metric through symmetry breaking.
Abstract
We present a gauge theory of the super SL(2,C) group. The gauge potential is a connection of the Super SL(2,C) group. A MacDowell-Mansouri type of action is proposed where the action is quadratic in the Super SL(2,C) curvature and depends purely on gauge connection. By breaking the symmetry of the Super SL(2,C) topological gauge theory to SL(2,C), a metric is naturally defined.
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