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Light-Cone Wilson Loops and the String/Gauge Correspondence

Yuri Makeenko

TL;DR

The paper investigates a Π-shaped light-cone Wilson loop in ${\cal N}=4$ SYM and its open-string dual in $AdS_5\times S^5$, connecting perturbative anomalous dimensions of twist-two operators to minimal-surface predictions and testing the GKP result at large $\\lambda$. It develops both the gauge-theory perturbative framework, yielding $\\gamma_n = {\\lambda}/{(2\\pi^2)}\\log n$ at order $\\lambda$, and the string-theory side, where the classical minimal surface reproduces the strong-coupling prediction $\\gamma_n = {\\sqrt{\\lambda}}/\\pi \,\\log n$. The work also highlights a quantum-mechanical interpretation of the minimal-surface saddle, involving tunneling in an effective potential, and discusses how cusp dynamics underpin the observed logarithmic behavior. Overall, the results reinforce the AdS/CFT correspondence for nontrivial Wilson-loop observables and motivate further higher-order and spectral explorations of open-string dynamics.

Abstract

We investigate a Π-shape Wilson loop in N=4 super Yang--Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous dimensions of conformal operators with large Lorentz spin and present an explicit calculation in perturbation theory to order λ. We find the minimal surface in the supergravity approximation, that reproduces the Gubser, Klebanov and Polyakov prediction for the anomalous dimensions at large λ=g_YM^2 N, and discuss its quantum-mechanical interpretation.

Light-Cone Wilson Loops and the String/Gauge Correspondence

TL;DR

The paper investigates a Π-shaped light-cone Wilson loop in SYM and its open-string dual in , connecting perturbative anomalous dimensions of twist-two operators to minimal-surface predictions and testing the GKP result at large . It develops both the gauge-theory perturbative framework, yielding at order , and the string-theory side, where the classical minimal surface reproduces the strong-coupling prediction . The work also highlights a quantum-mechanical interpretation of the minimal-surface saddle, involving tunneling in an effective potential, and discusses how cusp dynamics underpin the observed logarithmic behavior. Overall, the results reinforce the AdS/CFT correspondence for nontrivial Wilson-loop observables and motivate further higher-order and spectral explorations of open-string dynamics.

Abstract

We investigate a Π-shape Wilson loop in N=4 super Yang--Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous dimensions of conformal operators with large Lorentz spin and present an explicit calculation in perturbation theory to order λ. We find the minimal surface in the supergravity approximation, that reproduces the Gubser, Klebanov and Polyakov prediction for the anomalous dimensions at large λ=g_YM^2 N, and discuss its quantum-mechanical interpretation.

Paper Structure

This paper contains 10 sections, 63 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Light-cone Wilson loop in SYM
  3. The set up
  4. Extension to ${\cal N}=4$ SYM
  5. Order $\lambda$ of perturbation theory
  6. Remark on cusp near the light cone
  7. Open string in $AdS_5\times S^5$
  8. Finding the minimal surface
  9. Quantum-mechanical interpretation
  10. Conclusion

Figures (4)

  • Figure 1: $\Pi$-shape Wilson loop. The segment $[0,y^\mu\!=\!v^\mu T]$ lies at the light cone. The loop is analytically given by Eq. (\ref{['parametrized']}).
  • Figure 2: Diagrams of the order $\lambda$ for the expectation value of the $\Pi$-shape Wilson loop. The dashed lines represent either scalar or gauge-field propagators. Only the diagrams in Figs. (b) and (e) contribute to the anomalous dimension $\gamma_n$.
  • Figure 3: $\Gamma$-shape Wilson loop having a cusp. The cusp angle $\gamma$ is given by Eq. (\ref{['cuspangle']}).
  • Figure 4: $\Pi$-shape loop (a) bounding the minimal surface. The rotated segment lies at the light cone. The $\log^2$-term comes from the region near the cusp which is magnified in (b). There are two such regions associated with the two cusps. The typical size of the magnified region is $\sim L$.