Gauge- xing on the Lattice via Orbifolding

When xing a covariant gauge, most popularly the Landau gauge, on the lattice one encounters the Neuberger 0/0 problem which prevents one from formulating a Becchi Rouet Stora Tyutin symmetry on the lattice. Following the interpretation of this problem in terms of Witten-type topological eld theory and using the recently developed Morse theory for orbifolds, we propose a modi cation of the lattice Landau gauge via orbifolding of the gaugexing group manifold and show that this modi cation circumvents the orbit-dependence issue and hence can be a viable candidate for evading the Neuberger problem. Using algebraic geometry, we also show that though the previously proposed modi cation of the lattice Landau gauge via stereographic projection relies on delicate departure from the standard Morse theory due to the non-compactness of the underlying manifold, the corresponding gaugexing partition function turns out to be orbit independent for all the orbits except in a region of measure zero.