On the doubling phenomenon in lattice Chern-Simons theories

We analyse the pure Chern-Simons theory on an Euclidean infinite lattice. W e point out that, as a consequence of its symmetries, the Chern-Simons theo ry does not have an integrable kernel. Due to the linearity of the action i n the derivatives, the situation is very similar to the one arising in the lattice formulation of fermionic theories. Doubling of bosonic degrees of f reedom is removed by adding a Maxwell term with a mechanism similar to the one proposed by Wilson for the fermionic theories.