Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3

TL;DR

This paper calculates the one-loop quantum correction to the energy of a spinning string in AdS_4 x CP^3, providing insights into the cusp anomalous dimension and its discrepancy with Bethe ansatz predictions.

Contribution

It derives the one-loop correction for a folded spinning string in AdS_4 x CP^3 and explores its implications for the cusp anomalous dimension.

Findings

One-loop correction to the cusp anomalous dimension is -5 log 2/(2π).

Discrepancy found between this correction and Bethe ansatz predictions.

Results contribute to understanding quantum corrections in AdS/CFT correspondence.

Abstract

We derive the one-loop correction to the space-time energy of a folded string in AdS_4 x CP^3 carrying spin S in AdS_4 and angular momentum J in CP^3 in the long string approximation. From this general result in the limit J << log S we obtain the one-loop correction to the cusp anomalous dimension which turns out to be -5 log 2/(2\pi). This value appears to be in conflict with the prediction from the recently conjectured all-loop Bethe ansatz.