Analytic determination of the SU2 lattice gauge theory stable under Migdal-Kadanoff renormalization

The Migdal-Kadanoff recursion relations are applied to the most general plaquette action. The stable action, determined by a weak-coupling expansion, lies between the Manton and the heat kernel ones, in agreement with previous numerical investigations. Moreover, it is shown that certain contributions to the renormalization of the coupling constant exactly coincide with the perturbative ones; this happens for those terms of pure group-theoretical origin, which are the same in the perturbative expansions of the 4D gauge theory and of the corresponding 2D chiral model