Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT

TL;DR

The paper computes the 1-loop correction $E_1$ to the energy of a folded $(S,J)$ string in $AdS_5 \times S^5$ in the long-string limit $S\gg J \gg 1$, providing a strong-coupling interpretation of the anomalous dimensions of higher-twist SL(2) sector operators. It derives a closed expression $E_1 = \frac{J}{\sqrt{\lambda}}\sqrt{1+x^2}\,F(x) + O(\kappa^0)$ with $x = \frac{\sqrt{\lambda}}{\pi J}\ln\frac{S}{J}$ and $\kappa = \frac{J}{\sqrt{\lambda}}\sqrt{1+x^2}$, and shows that $E_1$ interpolates between the known $\ln S$ behavior at large $S/J$ and the $\lambda/J^2\ln^3(S/J)$ regime, consistent with both gauge-theory thermodynamic-limit corrections and the Bethe ansatz S-matrix phase. The results reinforce the universality of the $\ln S$ coefficient in the strong-coupling expansion and highlight non-analytic corrections tied to the dressing phase, offering a nontrivial cross-check for the AdS/CFT correspondence and guiding future multi-loop and multi-spin investigations.

Abstract

We compute 1-loop correction E_1 to the energy of folded string in AdS_5 x S^5 (carrying spin S in AdS_5 and momentum J in S^5) using ``long string'' approximation in which S >> J >> 1. According to AdS/CFT E_1 should represent the first subleading correction to strong coupling expansion of anomalous dimension of higher twist SL(2) sector operators of the form Tr D^S Z^J. We show that E_1 smoothly interpolates between the ln S regime (previously found in the J=0 case) and the λ/J^2 ln^3 (S/J) regime (which is the leading correction to the thermodynamic limit on the spin chain side). This supports the universality of the ln S scaling. As in previous work, we also find ``non-analytic'' corrections related to non-trivial 1-loop phase in the corresponding Bethe ansatz S-matrix.

Figures (1)

• Figure 1: Plot of the function $\sqrt{1+x^2}F(x)$