Quantum string integrability and AdS/CFT

TL;DR

This paper investigates the persistence of integrable structures in string theory within the AdS/CFT correspondence, providing evidence that quantum corrections do not break integrability and establishing a connection with gauge theory spin chains.

Contribution

It demonstrates that integrability in classical string theory on AdS_5 x S^5 persists at the quantum level beyond tree approximation, with explicit calculations of conserved charges.

Findings

Quantum string fluctuations preserve integrability to quartic order.

Explicit construction of higher conserved charges using Lax representation.

Matching of string theory charges with gauge theory spin chain spectra.

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.