Quantum string integrability and AdS/CFT

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.

arXiv commentv2: references and typos corrected; v3: minor corrections and comments, 23 pages

References in corpus (38)

• Gauge Theory Correlators from Non-Critical String Theory
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• A semi-classical limit of the gauge/string correspondence
• Type IIB superstring action in AdS_5 x S^5 background
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• Bethe Ansatz for Quantum Strings
• Exactly solvable model of superstring in Ramond-Ramond plane wave background
• How Algebraic Bethe Ansatz works for integrable model
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Classical/quantum integrability in AdS/CFT
• Multi-spin string solutions in AdS_5 x S^5
• The su(2|3) Dynamic Spin Chain
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Aspects of Semiclassical Strings in AdS${}_5$
• Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Matching Higher Conserved Charges for Strings and Spins
• Spinning strings and AdS/CFT duality
• Near Horizon Superspace
• Holography Beyond the Penrose Limit
• Simplifying superstring action on AdS_5 x S^5
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Superstring action in AdS_5 x S^5: kappa symmetry light cone gauge
• Strings in the near plane wave background and AdS/CFT
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Higher loops, integrability and the near BMN limit
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• Non-local charges on AdS_5 x S^5 and PP-waves
• Light cone gauge formulation of IIB supergravity in $Ad{S}_5\times S^5$ background and AdS/CFT correspondence
• Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5
• Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions
• On the Integrability of String Theory in AdS_5 x S^5

Cited by in corpus (28)

• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Quantum Consistency of the Superstring in AdS_5 x S^5 Background
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Integrable open spin chains from giant gravitons
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• Wrapping interactions and the genus expansion of the 2-point function of composite operators
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• The Algebra of Transition Matrices for the AdS_5 x S^5 Superstring
• Classical Open String Integrability
• The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge
• Flat Currents of the Green-Schwarz Superstrings in AdS_5 x S^1 and AdS_3 x S^3 backgrounds
• On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory
• Integrable Open Spin Chains and the Doubling Trick in N = 2 SYM with Fundamental Matter
• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
• Wound and Rotating Strings in AdS_5 x S^5
• Open string integrability and AdS/CFT
• Notes on fast moving strings
• Plane wave limit of local conserved charges
• Sugawara form for AdS superstring
• A review of integrable deformations in AdS/CFT
• BRST Invariance of Non-local Charges and Monodromy Matrix of Bosonic String on AdS(5)xS(5)
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Wrapping effects in supersymmetric gauge theories