The existence of a nontrivial interpolating function h(\lambda) is one of the
novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At
strong coupling, most of the investigation of semiclassical effects so far has
been for strings in the AdS4 sector. Several cutoff prescriptions have been
proposed, leading to different predictions for the constant term in the
expansion h(\lambda)=\sqrt{\lambda/2} + c + ... . We calculate quantum
corrections for giant magnons, using the algebraic curve, and show by comparing
to the dispersion relation that the same prescriptions lead to the same values
of c in this CP3 sector. We then turn to finite-J effects, where a comparison
with the Luescher F-term correction shows a mismatch for one of the three sum
prescriptions. We also compute some dyonic and higher F-terms for future
comparisons.Comment: 30 pages, 1 figure, 1 table. v2 has minor improvements to the text,
and extra references. v3 has further textual changes, version to appear in
JHE
