Scattering of Giant Holes

TL;DR

The paper investigates two-giant-hole scattering in the $\mathfrak{sl}(2)$ sector of $\mathcal{N}=4$ SYM and its AdS/CFT dual on the GKP string. It derives the all-loop hole S-matrix from the asymptotic Bethe ansatz with the BES dressing, and presents a strong-coupling description whose phase is compactly expressed in terms of Zhukovsky variables; at the same time, it computes the worldsheet S-matrix semiclassically from soliton time delays on the GKP string. The key result is the exact agreement between the gauge-theory phase $\delta_{\rm spin}$ and the string-theory phase $\delta_{\rm string}$ in the strong-coupling limit, providing a nontrivial test of integrability across the AdS/CFT dictionary. The work also outlines how these two-hole results generalize to multi-hole states and arbitrary string lengths, offering a practical alternative to the full all-loop ABA for exploring the spectrum of large-spin operators in the non-compact $SL(2)$ sector.

Abstract

We study scalar excitations of high spin operators in N=4 super Yang-Mills theory, which are dual to solitons propagating on a long folded string in AdS_3 x S^1. In the spin chain description of the gauge theory, these are associated to holes in the magnon distribution in the sl(2,R) sector. We compute the all-loop hole S-matrix from the asymptotic Bethe ansatz, and expand in leading orders at weak and strong coupling. The worldsheet S-matrix of solitonic excitations on the GKP string is calculated using semiclassical quantization. We find an exact agreement between the gauge theory and string theory results.