Semiclassical strings and AdS/CFT

TL;DR

This work presents a coherent-state, semiclassical framework for AdS/CFT in sectors with large quantum numbers, showing how the spin-chain dilatation operator in ${\cal N}=4$ SYM and the classical string action on $AdS_5\times S^5$ converge to identical Landau-Lifshitz-type sigma models in the appropriate large-charge limit. It demonstrates leading-order energy/dimension matching across multiple sectors (e.g., SU(2), SU(3), SL(2)) and explains the emergence of integrable structures and coherent operators that relate string profiles to SYM states. The analysis covers BMN-like near-BPS states, multispin configurations, and fast-motion regimes in $S^5$, while addressing higher-order corrections and the role of wrapping effects in reconciling discrepancies at ${\tilde{\lambda}}^3$ order. Overall, the paper highlights a universal bridge between semiclassical strings and long SYM operators via coherent-state effective actions, underpinned by integrability and the planar limit. This framework provides a concrete path toward understanding the string/gauge duality beyond BPS sectors and toward an all-order characterization of the planar spectrum in a subsector of ${\cal N}=4$ SYM.

Abstract

We discuss AdS/CFT duality in the sector of ``semiclassical'' string states with large quantum numbers. We review the coherent-state effective action approach, in which similar 2d sigma model actions appear from the AdS_5 x S^5 string action and from the integrable spin chain Hamiltonian representing the N=4 super Yang-Mills dilatation operator. We consider mostly the leading-order terms in the energies/anomalous dimensions which match but comment also on higher-order corrections.