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Comment on the Scaling Function in AdS4 x CP3

Nikolay Gromov, Victor Mikhaylov

TL;DR

The paper analyzes the one-loop energy correction for the folded spinning string in AdS4 x CP3 within the AdS4/CFT3 context. It employs the finite-gap algebraic curve to compute fluctuation frequencies and introduces a physically motivated heavy-light regularization of the fluctuation sum. This regularization produces a one-loop energy that precisely matches the all-loop Bethe equations and reproduces the known scaling function in the large spin limit, providing a nontrivial consistency check of the integrable structure. The work strengthens confidence in the AdS4 x CP3 algebraic curve and its encoded quantum corrections, and suggests directions for connecting the regularization to the worldsheet action and to the Frolov-Tseytlin limit.

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.

Comment on the Scaling Function in AdS4 x CP3

TL;DR

The paper analyzes the one-loop energy correction for the folded spinning string in AdS4 x CP3 within the AdS4/CFT3 context. It employs the finite-gap algebraic curve to compute fluctuation frequencies and introduces a physically motivated heavy-light regularization of the fluctuation sum. This regularization produces a one-loop energy that precisely matches the all-loop Bethe equations and reproduces the known scaling function in the large spin limit, providing a nontrivial consistency check of the integrable structure. The work strengthens confidence in the AdS4 x CP3 algebraic curve and its encoded quantum corrections, and suggests directions for connecting the regularization to the worldsheet action and to the Frolov-Tseytlin limit.

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.

Paper Structure

This paper contains 4 sections, 24 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Algebraic Curve for the Folded String
  3. Summation Prescription
  4. Summary

Figures (2)

  • Figure 1: Equation relating fermionic and bosonic fluctuations (2,5) and (2,9). Adding a pole with double residue between sheets 2 and 9 is equivalent to adding a (2,5) pole plus a (2,6) pole. The fermionic fluctuations with polarizations (2,5) and (2,6) are equivalent since $q_5=q_6$.
  • Figure 2: Equation relating fluctuations inside ${\mathbb C \mathbb P}^3$ with polarizations (3,7) and (3,5). The (3,7) fluctuation can be decomposed into a (3,5) fluctuation plus (4,7) fluctuation. The fluctuations (3,5) and (4,7) for the folded string are obviously equivalent.