Comment on the Scaling Function in AdS4 x CP3

TL;DR

This paper verifies the one-loop energy spectrum of a folded spinning string in AdS4 x CP3 using algebraic curve methods, confirming consistency with all-loop Bethe equations and supporting the integrability framework of AdS4/CFT3.

Contribution

It reproduces previous fluctuation spectrum results with algebraic curve techniques and confirms their agreement with Bethe ansatz predictions in AdS4/CFT3.

Findings

One-loop energy matches Bethe ansatz predictions after resummation.

Algebraic curve method effectively reproduces fluctuation spectra.

Supports the integrability-based all-loop Bethe equations for AdS4/CFT3.

Abstract

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.