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.