  We develop semiclassical methods to analyze the spectrum of BPS monopole
operators for superconformal field theories in three dimensions with N=2
supersymmetry. We show that the chiral ring of the theory results from the
semiclassical holomorphic quantization of the solution of classical BPS
equations of motion on the cylinder. We apply this formalism to various
theories. We also use these techniques to compare the chiral rings of theories
that might be related to each other via Seiberg dualities in four dimensions.
We find that the change of basis transformations that generate dualities in
four dimensions (homological operations) generically do not work in three
dimensions in the presence of Chern-Simons terms. Instead, new theories
generally arise this way. When dualities are possible, the Chern-Simons
couplings need to satisfy certain arithmetic congruences. We also determine the
spectrum of R-charges of the chiral ring operators by assembling them on a
Hilbert series and by minimizing the coefficient of the maximum pole relative
to the trial R-charge. This is related to volume minimization in theories with
dual supergravity setups.
