The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus

We study the BPS spectrum of monopole operators in ABJM theory. First we work out the complete spectrum of the chiral ring by using a semiclassical analysis of the field theory compactified on a two sphere. By properly taking into account the full quantization condition of monopole charges, we show that the moduli space of ABJM theory with Chern-Simons level k, -k is a particular Z_k cover of the symmetric product of C^4/Z_k. We also work out in detail the spectrum of fluctuations around half-BPS monopole configurations and we find candidate states for a dual BPS configuration to the giant torus solution found by Nishioka and Takayanagi in the supergravity limit. We also discuss more general BPS states.