Comment on the Scaling Function in AdS4 x CP3

The folded spinning string in AdS3 gives us an important insight into AdS/CFT duality. Recently its one-loop energy was analyzed in the context of AdS4/CFT3 by McLoughlin and Roiban arXiv:0807.3965, by Alday, Arutyunov and Bykov arXiv:0807.4400 and by Krishnan arXiv:0807.4561. They computed the spectrum of the fluctuations around the classical solution. In this paper we reproduce their results using the algebraic curve technique and show that under some natural resummation of the fluctuation energies the one-loop energy agrees perfectly with the predictions of arXiv:0807.0777. This provides a further support of the all-loop Bethe equations and of the AdS4xCP3 algebraic curve developed in arXiv:0807.0437.