Giant magnons in AdS_4/CFT_3: dispersion, quantization and finite--size corrections

We study giant magnon solutions in AdS4 \times CP3. We compute quantum corrections to their dispersion relation. We find out that the one--loop correction vanishes in infinite volume. This implies that the interpolating function h(\lambda) between strong and weak coupling regimes does not have a constant term \lambda^0 at strong coupling. We also compute first nonvanishing finite volume correction to the one--loop expression. When compared to the L\"{u}sher formula, our results could provide a nontrivial check of the AdS4 \times CP3 S--matrix proposed recently in arXiv:0807.1924.