General covariance, and supersymmetry without supersymmetry

TL;DR

This paper introduces a novel four-dimensional gauge theory with covariance and supersymmetry properties, revealing that local supersymmetry emerges from Yang-Mills symmetry and suggesting classical integrability and potential non-perturbative quantization methods.

Contribution

It presents an unusual covariant supersymmetric SU(2) gauge theory where local supersymmetry arises from Yang-Mills symmetry, and explores its integrability and quantization.

Findings

The theory has propagating degrees of freedom.

Local supersymmetry is a consequence of Yang-Mills symmetry.

The theory is classically integrable.

Abstract

An unusual four-dimensional generally covariant and supersymmetric SU(2) gauge theory is described. The theory has propagating degrees of freedom, and is invariant under a local (left-handed) chiral supersymmetry, which is half the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the theory reveals the remarkable feature that the local supersymmetry is a consequence of Yang-Mills symmetry, in a manner reminiscent of how general coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills symmetry. It is possible to write down an infinite number of conserved currents, which strongly suggests that the theory is classically integrable. A possible scheme for non-perturbative quantization is outlined. This utilizes ideas that have been developed and applied recently to the problem of quantizing gravity.