Gravitation as a Supersymmetric Gauge Theory

TL;DR

This paper develops a gauge theory of gravity based on the Super SL(2,C) group, connecting it to general relativity through symmetry breaking and auxiliary fields, and relates it to Ashtekar variables.

Contribution

It introduces a supersymmetric gauge formulation of gravity using Super SL(2,C), proposing a quadratic action and symmetry breaking to recover Einstein's theory.

Findings

The theory reduces to general relativity with an auxiliary spinor field.

A connection to Ashtekar variables is established.

The auxiliary spinor plays a role similar to the Witten spinor in energy proofs.

Abstract

We propose a gauge theory of gravitation. 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 spinor metric is naturally defined. With an auxiliary anti-commuting spinor field, the theory is reduced to general relativity. The Hamiltonian variables are related to the ones given by Ashtekar. The auxiliary spinor field plays the role of Witten spinor in the positive energy proof for gravitation.