  In this letter we calculate the exact partition function for free bosons on
the plane with lacunae. First the partition function for a plane with two
spherical holes is calculated by matching exactly for the infinite set of
Wilson coefficients in an effective world line theory and then performing the
ensuing Gaussian integration. The partition is then re-calculated using
conformal field theory techniques, and the equality of the two results is made
manifest. It is then demonstrated that there is an exact correspondence between
the Wilson coefficients (susceptabilities) in the effective field theory and
the weights of the individual excitations of the closed string coherent state
on the boundary. We calculate the partition function for the case of three
holes where CFT techniques necessitate a closed form for the map from the
corresponding closed string pants diagrams. Finally, it is shown that the
Wilson coefficients for the case of quartic and higher order kernels, where
standard CFT techniques are no longer applicable, can also be completely
determined. These techniques can also be applied to the case of non-trivial
central charges.

High Energy Physics - Theory;Statistical Mechanics;High Energy Physics - Phenomenology