We develop a constructive renormalization group framework for lattice gauge theories formulated in terms of surface-based models on Z⁴ with gauge group SU (2). The approach is based on a multiscale block transformation acting on ensembles of closed surfaces weighted by plaquette amplitudes and recoupling (6j) symbols. We construct a polymer function space with a Banach norm providing exponential control of activities and prove convergence of the cluster expansion with explicit constants. The renormalization group map is shown to be well-defined, finite-range, and strictly contracting on irrelevant interactions. A key mechanism is a uniform exponential suppression arising from 6j-symbol orthogonality, which induces monotone growth of the surface tension along the flow. As a consequence, we establish asymptotic freedom of the running coupling, tightness of the induced measures, and exponential decay of truncated correlations. These results provide a self-contained constructive framework with explicit multiscale control, advancing the rigorous analysis of four-dimensional lattice gauge theories.
Plinio Pacheco Junior (Thu,) studied this question.