Open string fluctuations in AdS_5xS^5 and operators with large R-charge

TL;DR

This work provides a semiclassical string computation of the OPE coefficients $c_J(\lambda)$ for a circular Wilson loop in ${\cal N}=4$ SYM in the regime of large R-charge $J$, extending beyond the supergravity limit to all orders in the $\alpha'$ expansion. The leading strong-coupling result matches field-theory predictions and exhibits exponential suppression in $J^2/\sqrt{\lambda}$, with a BMN-consistent exponent $S_{cl}=\sqrt{\lambda}[1-\sqrt{j^2+1}-j\ln(\sqrt{j^2+1}-j)]$ for $j=J/\sqrt{\lambda}$. In the perturbative and BMN regimes the calculations reproduce known limits: a double-scaling form $c_J(\lambda)\sim\frac{1}{2}\sqrt{J\lambda}\exp(-\frac{J^2}{2\sqrt{\lambda}})$ and a perturbative behavior $\langle W(C)\mathcal{O}_J(x)\rangle\propto\frac{\lambda^{J/2}}{J!}$, respectively. The results demonstrate a controlled interpolation between weak and strong coupling for open-string observables and suggest a path to relating planar SYM diagrams to semiclassical string worldsheets.

Abstract

A semiclassical string description is given for correlators of Wilson loops with local operators in N=4 SYM theory in the regime when operators carry parametrically large R-charge. The OPE coefficients of the circular Wilson loop in chiral primary operators are computed to all orders in the alpha' expansion in AdS_5xS^5 string theory. The results agree with field-theory predictions.

Figures (2)

• Figure 1: The semiclassical expansion of $\left\langle \phi^n \right\rangle$ to order $O(\hbar^2)$. The first two diagrams are of order $\hbar n^2$ and $\hbar^2n^4$, respectively. The loop corrections (c) and (d) are of order $\hbar^2n^2$ and are down by a factor of $n^2$ compared to (a) and (b).
• Figure 2: The classical string world sheet (\ref{['mins2']}) for different values of angular momentum.