The color-flavor transformation of induced QCD

The color-flavor transformation is applied to the $U(N_c)$ lattice model, in which the gauge theory is induced by the chiral scalar field associated with an elementary plaquette. The flavor degrees of freedom are related with the number of generations of the auxiliary field, and flavor components of each generation are associated with all the plaquettes having a lattice site in common. The property of the dual color-flavor transformed theory, which is expressed in terms of the gauge singlets, are analyzed in $d=2$ and $d=3$ dimensions. The saddle point solution of the model in the large-$N_c$ limit is discussed. The correlations between the plaquettes, which are described by the dual theory, allows to define the dual lattice. In $d=3$ dimensions it is made of tetradecahedra which correspond to the cubes of the original lattice. The continuum limit of $d=2$ effective theory is discussed.