Spinning strings at one-loop in AdS_4 x P^3

TL;DR

The authors compute the one-loop quantum correction to the energy of a folded spinning string in AdS$_4$×$\mathbb{P}^3$, carrying spin $S$ in AdS$_4$ and angular momentum $J$ in CP$^3$, in the scaling regime where $S,J\to\infty$ with $\ell=J/(2\ln S)$ fixed. They derive the fluctuation spectrum (bosonic and fermionic) in this limit and obtain explicit expressions for the one-loop energy $E_1$ in the cases $J=0$ and $J\neq0$, showing that $E_1$ scales with $\ln S$ and computing the generalized scaling function. A key result is that the leading strong-coupling term agrees with expectations for the universal scaling function, but the subleading term in the generalized scaling function disagrees with the conjectured all-loop Bethe Ansatz predictions for the AdS$_4$/CFT$_3$ duality, suggesting possible corrections to the dressing phase or to integrability at subleading order. The work highlights the need for further checks, including higher-loop calculations and a deeper understanding of the AdS$_4$/CFT$_3$ integrable structure, to reconcile string-theory results with Bethe Ansatz predictions. The findings provide a concrete semiclassical testbed for the AdS$_4$/CFT$_3$ correspondence and illuminate the structure of strong-coupling corrections in this lower-dimensional holographic dual.

Abstract

We analyze the folded spinning string in AdS_4 x P^3 with spin S in AdS_4 and angular momentum J in P^3. We calculate the one-loop correction to its energy in the scaling limit of both ln S and J large with their ratio kept fixed. This result should correspond to the first subleading strong coupling correction to the anomalous dimension of operators of the type Tr(D^S(Y^\dagger Y)^J) in the dual N=6 Chern-Simons-matter theory. Our result appears to depart from the predictions for the generalized scaling function found from the all-loop Bethe equations conjectured for this AdS_4/CFT_3 duality. We comment on the possible origin of this difference.