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A Test of the AdS/CFT Correspondence Using High-Spin Operators

M. K. Benna, S. Benvenuti, I. R. Klebanov, A. Scardicchio

TL;DR

This work tests the AdS/CFT correspondence for high-spin operators by numerically solving the Beisert-Eden-Staudacher integral equation that encodes the universal function f(g). The authors implement a matrix-based numerical approach using a truncated mode expansion to obtain a smooth f(g) that agrees with the strong-coupling predictions from semiclassical strings in $AdS_5$, including a precise leading two-term match and a numerical prediction for the $1/g$ correction. They also analyze the analytic structure of f(g), finding branch points on the imaginary axis and suggesting a rich multi-cut behavior. Overall, the results provide a nontrivial validation of AdS/CFT for a non-BPS observable and offer detailed insights into the strong-coupling expansion and its analytic properties.

Abstract

In two remarkable recent papers, hep-th/0610248 and hep-th/0610251, the complete planar perturbative expansion was proposed for the universal function of the coupling, f(g), appearing in the dimensions of high-spin operators of the N=4 SYM theory. We study numerically the integral equation derived in hep-th/0610251, which implements a resummation of the perturbative expansion, and find a smooth function that approaches the asymptotic form predicted by string theory. In fact, the two leading terms at strong coupling match with high accuracy the results obtained for the semiclassical folded string spinning in $AdS_5$. This constitutes a remarkable confirmation of the AdS/CFT correspondence for high-spin operators, and equivalently for the cusp anomaly of a Wilson loop. We also make a numerical prediction for the third term in the strong coupling series.

A Test of the AdS/CFT Correspondence Using High-Spin Operators

TL;DR

This work tests the AdS/CFT correspondence for high-spin operators by numerically solving the Beisert-Eden-Staudacher integral equation that encodes the universal function f(g). The authors implement a matrix-based numerical approach using a truncated mode expansion to obtain a smooth f(g) that agrees with the strong-coupling predictions from semiclassical strings in , including a precise leading two-term match and a numerical prediction for the correction. They also analyze the analytic structure of f(g), finding branch points on the imaginary axis and suggesting a rich multi-cut behavior. Overall, the results provide a nontrivial validation of AdS/CFT for a non-BPS observable and offer detailed insights into the strong-coupling expansion and its analytic properties.

Abstract

In two remarkable recent papers, hep-th/0610248 and hep-th/0610251, the complete planar perturbative expansion was proposed for the universal function of the coupling, f(g), appearing in the dimensions of high-spin operators of the N=4 SYM theory. We study numerically the integral equation derived in hep-th/0610251, which implements a resummation of the perturbative expansion, and find a smooth function that approaches the asymptotic form predicted by string theory. In fact, the two leading terms at strong coupling match with high accuracy the results obtained for the semiclassical folded string spinning in . This constitutes a remarkable confirmation of the AdS/CFT correspondence for high-spin operators, and equivalently for the cusp anomaly of a Wilson loop. We also make a numerical prediction for the third term in the strong coupling series.

Paper Structure

This paper contains 3 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Numerical study of the integral equation
  3. Discussion

Figures (1)

  • Figure 1: Plot of the solutions of the integral equations: $f_m(g)$ for the ES kernel $K^{(m)}$ (upper curve, red), $f_0(g)$ for the kernel $K^{(m)} + K^{(c)}$ (middle curve, green), and $f(g)$ for the BES kernel $K^{(m)} + 2K^{(c)}$ (lower curve, blue). Notice the different asymptotic behaviors. The inset shows the three functions in the crossover region $0<g<1$.