Highly-improved lattice field-strength tensor

We derive an O(a^4)-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 O(a^4)-improved topological charge and action operators. 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.