The fermion determinant and the chiral gauge theory on a lattice
  Considering as an example a simple lattice ansatz for the chiral fermion determinant, we demonstrate that even very mild violation of gauge invariance by the determinant at finite lattice spacing leads to the need for another scale in the full gauge theory. This new scale is much grater than the lattice spacing and is associated with the gauge variables. 
S. V. Zenkin (INR, Moscow)