Volume-Independent Local Transfer Gap for Strong-Coupling Lattice Gauge Theory via Poincaré-Dobrushin Machinery
Year: 2026
Type: preprint
Abstract: DRAFT version. This is an advanced draft and remains subject to revision. The continuum Yang-Mills mass gap is not claimed as fully proved; the paper establishes strong-coupling lattice gap machinery and formulates the continuum transfer as a conditional RG/OS-transfer problem. We prove a volume-independent spectral gap for SU(N) lattice gauge theory in the strong-coupling regime using Holley–Stroock and Dobrushin–Zegarlinski tensorisation. For SU(2) in d=4 the tanh-based threshold is β < 2 artanh(1/6) ≈ 0.336. A restricted Poincaré inequality on typical sets gives a conditional route to improved scaling, but the continuum mass gap is not claimed as proved. The RG/continuum part is formulated as a conditional gap-transport programme requiring summable RG defects and quantitative typical-set transport on SU(N). CHANGELOG Changes in Version 2.2 (May 2026) Critical: Adversarial review 2026-05-07 integrated: the Kingman route was downgraded from a standalone mass-gap proof to a diagnostic plus summable-defect criterion; Wasserstein-RG is explicitly conditional on a new quantitative SU(N) typical-set transport theorem. Major: Post-Zookeeper transfer section added and synchronized in English/German: the lattice gap and area law are now framed as the main path, while Zookeeper and RFEP are used only as normal-form and transfer-checklist constraints, not as an automatic continuum proof. Major: RFEP v1.8 normal-form checklist integrated: the text now separates strong-coupling/lattice evidence from the still-open continuum/Osterwalder-Schrader transfer. Minor: Hyperref target prefixes added for stable combined-PDF links; stale build logs removed; EN/DE PDFs rebuilt and combined into a bilingual PDF. Files: Version 2.2 upload is prepared with English, German, and combined bilingual PDFs. Changes in Version 2.1 (March 2026) Major: Doeblin-minorisation analytical route to λ<0 (Remark rem:doeblin-analytical): 4-step programme reducing analytical proof to establishing Doeblin constant α(β)>0 for SU(2) block-spin kernel. Minor: Bougerol–Lacroix (1985) reference added. Minor: Duplicate label fix (eq:typical-set). Changes in Version 2.0 (March 2026) Critical: Fixed \thanks placement (was outside \author group).
Author: Geiger, Lukas
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7139052979