Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3

TL;DR

The paper performs a genuine field-theoretic semiclassical quantization of a folded string with spin S in AdS4 and angular momentum J in CP3, using the coset sigma-model for AdS4 × CP3. By analyzing quadratic fluctuations around the (S,J)-string in the long-string limit and fixing κ-symmetry, the authors derive bosonic and fermionic spectra, then compute the exact one-loop energy shift δE. In the slow-rotation regime J ≪ log S, δE reduces to a cusp-anomalous-dimension correction of δE ≈ −(5 log 2)/(2π) log(S/J), highlighting a discrepancy with the all-loop Bethe ansatz proposals. The work provides a self-contained, algebraic-curve-free verification of the strong-coupling correction and raises questions about the strong-coupling interpolation encoded in h(λ).

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/(2π). This value appears to be in conflict with the prediction from the recently conjectured all-loop Bethe ansatz.