Mass Gap of Four-Dimensional Lattice Yang–Mills Theory in a Forest Gauge

We fix the gauge of four-dimensional lattice Yang–Mills theory on a field of straight lines that meets every plaquette in exactly one link, so that each free link interacts with twelve others instead of eighteen. In this gauge the theory has a unique infinite-volume state with exponential decay of correlations and a positive mass gap at fixed lattice spacing, for SU(2) beyond the limit of every single-link argument in a gauge of this kind, by blocks made of the three free links of a plaquette, for every SU(N) beyond the curvature limit of the ungauged theory, and for SU(3) on a range more than two and a half times as large as was known before, where the same blocks raise the gap at the end of that range by two orders of magnitude and carry the range past it to $\beta_W=0.76$.