Open-Source Repository Explores 4D Yang–Mills Wilson Loops via Extended Bałaban Method

A publicly available GitHub repository titled "4D_Wilson_Loop_RG," maintained by Martin Peev and Akshunna S. Dogra, investigates the computation of correlation functions of physical observables in four-dimensional Yang–Mills (YM) theory. The project extends Bałaban's renormalisation group (RG) construction to the expectation of renormalised Wilson loops.

According to the project documentation, the initiative began on August 26, 2026, and seeks to address ultraviolet singular behaviours of Wilson loops and pointwise traces in dimensions greater than two. The researchers note that their ongoing work aims to identify scalar contributions corresponding to perimeter and corner renormalisations within the RG, targeting finite-volume constructions rather than infinite-volume limits.

Project Structure and Working Drafts

The repository provides several working drafts, manuscripts, and supporting notes:

• Manuscripts under Construction: Includes version V5 (PDF, LaTeX source, and bibliography) and its pedagogical companion summary (V4 companion), which serves as the current reference manuscript.
• Drafts and Reading Guides: Contains iteration drafts, cutoff-comparison documents, the D2 step map, IT-1 notes, and a Cauchy-estimate draft updated through October and November 2026.
• Verification Status: The authors state that mathematical content has been extensively checked with the assistance of Large Language Models (LLMs), but emphasize that nothing in the repository should be considered an academically rigorous, publishable mathematical paper.

Practical Implications and Verification

The repository is openly licensed under CC0-1.0 for original research material, while third-party contributions retain their respective notices. Interested researchers can verify the original announcements, build instructions, and LaTeX dependencies directly via the GitHub repository source.

To compile the documents, users require a recent TeX Live or MiKTeX installation equipped with pdfLaTeX, BibTeX, and latexmk, alongside the packages listed in the repository's dependency documentation.