Comparing strings in AdS(5)xS(5) to planar diagrams: an example

V. Pestun, K. Zarembo

TL;DR

The paper studies the correlator $igraket{W(C) O_J}ig$ of a Wilson loop with a local chiral primary operator in ${ t N}=4$ SYM, using its dual description as a semiclassical open string in $AdS_5 imes S^5$. By formulating a double-scaling limit with $j=J/\sqrt{\lambda}$, it develops a systematic $1/j^2$ expansion on the string side and compares it to the planar SYM perturbation theory, finding exact agreement at one loop and, for the leading large-$J$ sector, agreement to all orders in $\lambda/J^2$. The string calculation yields an explicit action expansion $S(j;C)=S_0+S_1/j^2+S_2/j^4+\cdots$ with computable coefficients, and the perturbative analysis confirms exponentiation of the dominant diagrams, matching the string-theory expectation $igraket{W(C) O_J(x)}ig brace \\sim |x|^{-2J} e^{-J S(j;C)}$. Together, these results reinforce that the same $\lambda/J^2$ parameter governs both descriptions, and they illustrate a remarkable, if nontrivial, consistency between semiclassical string dynamics and planar gauge-theory perturbation theory. The work also suggests practical advantages of the string approach for higher-order predictions in this regime.

Abstract

The correlator of a Wilson loop with a local operator in N=4 SYM theory can be represented by a string amplitude in AdS(5)xS(5). This amplitude describes an overlap of the boundary state, which is associated with the loop, with the string mode, which is dual to the local operator. For chiral primary operators with a large R charge, the amplitude can be calculated by semiclassical techniques. We compare the semiclassical string amplitude to the SYM perturbation theory and find an exact agrement to the first two non-vanishing orders.

Comparing strings in AdS(5)xS(5) to planar diagrams: an example

TL;DR

The paper studies the correlator

of a Wilson loop with a local chiral primary operator in

SYM, using its dual description as a semiclassical open string in

. By formulating a double-scaling limit with

, it develops a systematic

expansion on the string side and compares it to the planar SYM perturbation theory, finding exact agreement at one loop and, for the leading large-

sector, agreement to all orders in

. The string calculation yields an explicit action expansion

with computable coefficients, and the perturbative analysis confirms exponentiation of the dominant diagrams, matching the string-theory expectation

. Together, these results reinforce that the same

parameter governs both descriptions, and they illustrate a remarkable, if nontrivial, consistency between semiclassical string dynamics and planar gauge-theory perturbation theory. The work also suggests practical advantages of the string approach for higher-order predictions in this regime.

Abstract

The correlator of a Wilson loop with a local operator in N=4 SYM theory can be represented by a string amplitude in AdS(5)xS(5). This amplitude describes an overlap of the boundary state, which is associated with the loop, with the string mode, which is dual to the local operator. For chiral primary operators with a large R charge, the amplitude can be calculated by semiclassical techniques. We compare the semiclassical string amplitude to the SYM perturbation theory and find an exact agrement to the first two non-vanishing orders.