Wrapping interactions and a new source of corrections to the spin-chain/string duality

TL;DR

The paper investigates finite-size corrections in an integrable worldsheet framework for AdS/CFT, focusing on wrapping interactions arising from virtual particles around the cylinder. By analyzing Lüscher-type F- and μ-terms and employing the Thermodynamic Bethe Ansatz, it elucidates how these corrections emerge with nonstandard dispersion relations intrinsic to the worldsheet theory. In the near-BMN limit, it finds wrapping effects yield weak-coupling corrections of order $\lambda^L$ and strong-coupling corrections of the form $e^{-1/\sqrt{\lambda'}}$, offering a potential explanation for observed three-loop discrepancies and informing future quantum-string Bethe ansatz developments.

Abstract

Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an integrable {\em quantum} field theory, we deduce that there might be new corrections to the spin-chain/string Bethe ansatz paradigm. These come from virtual particles propagating around the circumference of the cylinder and render Bethe ansatz quantization conditions only approximate. We determine the nature of these corrections both at weak and at strong coupling in the near BMN limit, and find that the first corrections behave qualitatively as wrapping interactions at weak coupling.

Figures (1)

• Figure 1: The diagram to the left (the $\mu$-term) shows a particle splitting in two virtual, on-shell particles, traveling around the cylinder and recombining. The diagram to the right (the F-term) shows a virtual particle going around the circumference of the cylinder.