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May 22, 2026Open Access

Volume-Independent Spectral Gap for Strong-Coupling Lattice Gauge Theory via Poincar?-Dobrushin Machinery

Key Points

Establish a volume-independent spectral gap for SU(N) lattice gauge theory in the strong-coupling regime.
Utilized Holley–Stroock and Dobrushin–Zegarlinski tensorisation methods to prove the spectral gap.
Formulated continuum transfer as a conditional RG/OS-transfer problem.
Analyzed SU(2) in d=4 with a tanh-based threshold for β < 2 artanh(1/6) ≈ 0.336.
Demonstrated a volume-independent spectral gap for SU(N) lattice gauge theory under strong coupling conditions.
Conditional route to improved scaling through a restricted Poincaré inequality on typical sets.
Continued challenges in proving the continuum mass gap.

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 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 placement (was outside group).

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Lukas Geiger (Wed,) studied this question.

synapsesocial.com/papers/6a0ff42fd674f7c03778d5bb https://doi.org/https://doi.org/10.5281/zenodo.20315811

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