A semi-classical limit of the gauge/string correspondence

TL;DR

The paper develops a semiclassical, world-sheet sigma-model perspective on the gauge/string duality to study highly excited gauge-theory operators. By identifying soliton solutions on AdS_5×S^5 with large quantum numbers, it derives the dimension-spin relations for the leading Regge trajectory and other macroscopic string states, uncovering a characteristic logarithmic growth Δ − S ∼ (√λ/π) ln S at large spin. It also situates these results alongside perturbative logarithmic scaling and the cusp anomalous dimension, suggesting a deep connection between weak- and strong-coupling behavior. The analysis points to a broad applicability of sigma-model solitons to non-chiral, high-dimension operators and hints at extensions to non-conformal backgrounds and UV asymptotics.

Abstract

A world-sheet sigma model approach is applied to string theories dual to four-dimensional gauge theories, and semi-classical soliton solutions representing highly excited string states are identified which correspond to gauge theory operators with relatively small anomalous dimensions. The simplest class of such states are strings on the leading Regge trajectory, with large spin in AdS_5. These correspond to operators with many covariant derivatives, whose anomalous dimension grows logarithmically with the space-time spin. In the gauge theory, the logarithmic scaling violations are similar to those found in perturbation theory. Other examples of highly excited string states are also considered.

Figures (1)

• Figure 1: Short, long, and infinite strings spinning in $AdS_5$, shown here in cross-section.