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May 10, 2026Open Access

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

Key Points

The aim is to establish a volume-independent spectral gap for SU(N) lattice gauge theory using strong-coupling techniques.
Establish strong-coupling lattice gap machinery and continuum transfer as a conditional RG/OS-transfer problem.
Utilized Holley–Stroock and Dobrushin–Zegarlinski tensorisation methods to analyze the lattice gauge theory.
Formulated a conditional gap-transport programme requiring RG defects and typical-set transport on SU(N).
Proven a volume-independent spectral gap for SU(N) lattice gauge theory in the strong-coupling regime.
For SU(2) in d=4, determined the threshold for the mass gap as β < 2 artanh(1/6) ≈ 0.336.
Identified that the continuum mass gap is not fully proved, highlighting the need for further research.

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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