  The low energy $S$-matrix which describes non-relativistic scattering arising
from finite-range forces has UV/IR symmetries that are hidden in the
corresponding effective field theory (EFT) action. It is shown that the
$S$-matrix symmetries are manifest as geometric symmetries of the RG flow of
coupling constants in the EFT action in both three and two spatial dimensions.
An example is given demonstrating that UV/IR symmetry breaking in the
$S$-matrix implies strong constraints on the RG flow of the coefficients of the
corresponding symmetry-breaking operators in the EFT.
