  Using a generalized reciprocity relation between charge and vortex
conductivities at complex frequencies in two space dimensions, we identify the
capacitance in the insulating phase as a measure of vortex condensate
stiffness. We compute the ratio of boson superfluid stiffness to vortex
condensate stiffness at mirror points to be 0.21(1) for the relativistic O(2)
model. The product of dynamical conductivities at mirror points is used as a
test of charge-vortex duality. We propose the finite wave vector
compressibility as an experimental measure of the vortex condensate stiffness
for neutral lattice bosons.
