Highly improved lattice field-strength tensor

We derive an -improved lattice version of the continuum field-strength tensor. Discretization errors are reduced via the combination of several clover terms of various sizes, complemented by tadpole improvement. The resulting improved field-strength tensor is used to construct -improved topological charge and action operators. As a test of our improved field-strength tensor, we compare the values attained by these operators as we cool several configurations to self-duality with a previously defined highly improved action and assess the relative scale of the remaining discretization errors. We demonstrate accuracy to better than one part in 10,000.