  Recently, an asymptotic Bethe Ansatz that is claimed to describe anomalous
dimensions of "long" operators in the planar N=6 supersymmetric
three-dimensional Chern-Simons-matter theory dual to quantum superstrings in
AdS_4 x CP^3 was proposed. It initially passed a few consistency checks but
subsequent direct comparison to one-loop string-theory computations created
some controversy. Here we suggest a resolution by pointing out that, contrary
to the initial assumption based on the algebraic curve considerations, the
central interpolating function h(\lambda) entering the BMN or magnon dispersion
relation receives a non-zero one-loop correction in the natural string-theory
computational scheme. We consider a basic example which has already played a
key role in the AdS_5 x S^5 case: a rigid circular string stretched in both
AdS_4 and along an S^1 of CP^3 and carrying two spins. Computing the leading
one-loop quantum correction to its energy allows us to fix the constant
one-loop term in h(\lambda) and also to suggest how one may establish a
correspondence with the Bethe Ansatz proposal, including the non-trivial
one-loop phase factor. We discuss some problems which remain in trying to match
a part of world-sheet contributions (sensitive to compactness of the string
direction) and their Bethe Ansatz counterparts.
