A novel renormalizable representation of the Yang-Mills theory

TL;DR

The paper introduces a new renormalizable representation of Yang-Mills theory using two interacting fields, enabling better analysis of gauge-invariant correlators and low-energy observables like Wilson loops.

Contribution

It presents a reformulation of Yang-Mills theory with two fields that separates high- and low-energy degrees of freedom, facilitating infrared analysis and gauge-invariant observable evaluation.

Findings

Reformulation as a renormalizable two-field system.

Possibility to combine weak-coupling series with different methods.

Implementation of a fine-tuning condition to control field interactions.

Abstract

For a generic gauge-invariant correlator <{\cal Q}[A_{\mu}]>_{A}, we reformulate the standard D=4 Yang-Mills theory as a renormalizable system of two interacting fields a_{\mu} and B_{\mu} which faithfully represent high- and low-energy degrees of freedom of the single gauge field A_{\mu} in the original formulation. It opens a possibility to synthesize an infrared-nonsingular weak-coupling series, employed to integrate over a_{\mu} for a given background B_{\mu}, with qualitatively different methods. These methods are to be applied to evaluate the resulting (after the a_{\mu}-integration) representation of <{\cal Q}[A_{\mu}]>_{A} in terms of gauge-invariant generically non-local low-energy observables, like Wilson loops. The latter observables are averaged over B_{\mu} with respect to a gauge-invariant Wilsonean effective action S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy excitations, we implement a specific fine-tuning of the interaction between the pair of the fields: prior to the integration over B_{\mu}, the expectation value <a_{\mu}>_{a} vanishes, in the tree order of the loop-wise expansion, for an arbitrary configuration of B_{\mu}.