Perfect Gauge Actions on Anisotropic Lattices

On anisotropic lattices, where generally the lattice is rather coarse in spatial directions, a parametrized classically perfect action could help reducing lattice artifacts considerably. We investigate the possibility of constructing such actions for SU(3) gauge theory. We present two different methods to do so, either repeating the procedure used to create our newly parametrized isotropic FP action, or performing one single step starting with the isotropic result. The anisotropic action is parametrized using an ansatz including anisotropically APE-like smeared (``fat'') links. The parametrized classically perfect action with anisotropy $\xi=a_s/a_t=2$ is constructed and the renormalized anisotropy is measured using the torelon dispersion relation. It turns out that the renormalization is small.