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A note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature

Martin Kruczenski

TL;DR

The paper demonstrates that the large-spin anomalous dimension of twist-two operators in N=4 SYM can be obtained either from semiclassical rotating strings in AdS5 or from the cusp anomaly of Wilson loops in Minkowski AdS/CFT. By analytic continuation from Euclidean AdS and through a direct Minkowski-space calculation, the authors show the cusp contribution scales as ln S with a coefficient proportional to √(g_s N), matching the rotating-string result. They further argue that the Euclidean worldsheet determining the cusp is uniquely fixed by AdS symmetries, providing a symmetry-driven path to understand these results within the field theory. Overall, the work strengthens the proposed O_S ↔ rotating-string correspondence and highlights the central role of cusp anomalies in connecting gauge theory operators to string dynamics.

Abstract

Recently the anomalous dimension of twist two operators in N=4 SYM theory was computed by Gubser, Klebanov and Polyakov in the limit of large 't Hooft coupling using semi-classical rotating strings in AdS_5. Here we reproduce their results for large angular momentum by using the cusp anomaly of Wilson loops in Minkowski signature also computed within the AdS/CFT correspondence. In this case the anomalous dimension is related to an Euclidean worldsheet whose properties are completely determined by the symmetries of the problem. This gives support to the proposed identification of rotating strings and twist two operators.

A note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature

TL;DR

The paper demonstrates that the large-spin anomalous dimension of twist-two operators in N=4 SYM can be obtained either from semiclassical rotating strings in AdS5 or from the cusp anomaly of Wilson loops in Minkowski AdS/CFT. By analytic continuation from Euclidean AdS and through a direct Minkowski-space calculation, the authors show the cusp contribution scales as ln S with a coefficient proportional to √(g_s N), matching the rotating-string result. They further argue that the Euclidean worldsheet determining the cusp is uniquely fixed by AdS symmetries, providing a symmetry-driven path to understand these results within the field theory. Overall, the work strengthens the proposed O_S ↔ rotating-string correspondence and highlights the central role of cusp anomalies in connecting gauge theory operators to string dynamics.

Abstract

Recently the anomalous dimension of twist two operators in N=4 SYM theory was computed by Gubser, Klebanov and Polyakov in the limit of large 't Hooft coupling using semi-classical rotating strings in AdS_5. Here we reproduce their results for large angular momentum by using the cusp anomaly of Wilson loops in Minkowski signature also computed within the AdS/CFT correspondence. In this case the anomalous dimension is related to an Euclidean worldsheet whose properties are completely determined by the symmetries of the problem. This gives support to the proposed identification of rotating strings and twist two operators.

Paper Structure

This paper contains 6 sections, 67 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Rotating strings and Wilson loops
  3. Cusp anomaly from supergravity.
  4. Wilson loop in Minkowski signature
  5. Conclusions
  6. Acknowledgments

Figures (4)

  • Figure 1: Different ways to compute, at 1-loop, the anomalous dimension of the twist two operators in field theory for large spin. The straight lines indicate scalar propagators, wavy lines denote gluons and double lines a Wilson line in the adjoint representation. 1c) is just a Wilson line which can also be computed using the AdS/CFT.
  • Figure 2: Rotation of $f_0$ in the complex plane necessary to get an imaginary angle $\Theta$.
  • Figure 3: Wilson loop in the form of a wedge (thick lines). The thin lines show the light cone.
  • Figure 4: Sketch of the surface (in $AdS_5$) used to compute the Wilson loop of figure \ref{['fig:WlM']}.