Lattice Gauge Theories at Large

We investigate the lattice gauge theory with fermions at infinite coupling and show that, after formal integration over the fermion fields, it reduces to the Wilson pure gauge theory in the limit when the number of fermion flavours nf approaches infinity. When the boson fields are integrated over instead, the action describes a local theory of Fermi fields only. For finite nf the ferrnion action contains a finite number of terms.