Pregeometric First Order Yang-Mills Theory

TL;DR

This paper develops a first order formalism for Yang-Mills theory that remains consistent in a pregeometric regime where the metric degenerates, potentially paving the way for unification with gravity.

Contribution

It introduces a novel first order approach to Yang-Mills theory that can be extended to pregeometric phases, revealing new structures and interpretations.

Findings

First order formalism allows extension to degenerate metrics.

Fundamental vector/spinor substructure induces continuum magnetization.

Analogies with self-dual gravity suggest new unification paths.

Abstract

The standard description of particles and fundamental interactions is crucially based on a regular metric background. In the language of differential geometry, this dependence is encoded into the action via Hodge star dualization. As a result, the conventional forms of the scalar and Yang-Mills actions break down in a pregeometric regime where the metric is degenerate. This suggests the use of first order formalism, where the metric may emerge from more fundamental constituents and the theory can be consistently extended to the pregeometric phase. We systematically explore different realizations and interpretations of first order formalism, finding that a fundamental vector or spinor substructure brings about continuum magnetization and polarization as integration constants. This effect is analogous to the description of the cosmological dark sector in a recent self-dual formulation of gravity, and the similar form obtained for the first order Yang-Mills theory suggests new paths toward unification.