New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement

TL;DR

This paper introduces new lattice variable descriptions for SU(N) Yang-Mills theory, emphasizing the minimal option for SU(3) and its implications for understanding quark confinement via dual superconductivity.

Contribution

It presents a novel lattice variable framework for SU(N) Yang-Mills theory, highlighting the overlooked minimal option in SU(3) and its relevance to confinement mechanisms.

Findings

Validated new lattice descriptions for SU(2) and SU(3) Yang-Mills theories.

Identified the minimal option in SU(3) as a new approach.

Connected the framework to quark confinement via dual superconductivity.

Abstract

We give new descriptions of lattice SU(N) Yang-Mills theory in terms of new lattice variables. The validity of such descriptions has already been demonstrated in the SU(2) Yang-Mills theory by our previous works from the viewpoint of defining and extracting topological degrees of freedom such as gauge-invariant magnetic monopoles and vortices which play the dominant role in quark confinement. In particular, we have found that the SU(3) lattice Yang-Mills theory has two possible options, maximal and minimal: The existence of the minimal option has been overlooked so far, while the maximal option reproduces the conventional SU(3) Cho-Faddeev-Niemi-Shabanov decomposition in the naive continuum limit. The new description gives an important framework for understanding the mechanism of quark confinement based on the dual superconductivity.