Quantum string integrability and AdS/CFT

TL;DR

The paper investigates quantum integrability in type IIB string theory on AdS5xS5 and its relation to the integrable structure of planar N=4 SYM. It uses a semiclassical near-pp-wave expansion about point-like strings and a Lax-based construction to derive an infinite tower of local, mutually commuting bosonic charges, and computes their first several charges and spectra in AdS5 and S5 sectors. It then provides a concrete scheme to match these string charges to gauge-theory charges in the closed SU(2) sector via a fractional-power mapping and tests this against one-loop predictions, finding agreement in the O(1/J) corrections. The results support the persistence of integrability under quantum corrections and lay groundwork toward an exact, gauge/string dual integrable framework, while highlighting remaining gaps, such as higher-loop matching and the precise quantum-string Bethe ansatz.

Abstract

Recent explorations of the AdS/CFT correspondence have unveiled integrable structures underlying both planar N = 4 super-Yang-Mills theory and type IIB string theory on AdS_5 x S^5. Integrability in the gauge theory emerges from the fact that the dilatation generator can be identified with the Hamiltonian of an integrable quantum spin chain, and the classical string theory has been shown to contain infinite towers of hidden currents, a typical signature of integrability. Efforts to match the integrable structures of various classical string configurations to those of corresponding gauge theory quantum spin chains have been largely successful. By studying a semiclassical expansion about a class of point-like solitonic solutions to the classical string equations of motion on AdS_5 x S^5, we take a step toward demonstrating that integrability in the string theory survives quantum corrections beyond tree level. Quantum fluctuations are chosen to align with background curvature corrections to the pp-wave limit of AdS_5 x S^5, and we present evidence for an infinite tower of local bosonic charges that are conserved by the quantum theory to quartic order in the expansion. We explicitly compute several higher charges based on a Lax representation of the worldsheet sigma model and provide a prescription for matching the eigenvalue spectra of these charges with corresponding quantities descending from the integrable structure of the gauge theory.