Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case

TL;DR

This paper explores a classical mapping between massless scalar field theory and Yang-Mills theory, demonstrating that under a gradient expansion, both theories share similar spectra and solutions, confirming the mapping's validity.

Contribution

It provides a perturbative classical mapping between scalar and Yang-Mills theories using a gradient expansion with Lorentz covariance, establishing shared spectra and solutions.

Findings

The mapping exists at a perturbative level with gradient expansion.

Shared spectrum at leading order, similar to harmonic oscillator.

Constructed solutions confirm the extremum of the Yang-Mills action.

Abstract

We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of an harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.