A review of the AdS/CFT Quantum Spectral Curve

Abstract

We give an introduction to the Quantum Spectral Curve in AdS/CFT. This is an integrability-based framework which provides the exact spectrum of planar N = 4 super Yang-Mills theory (and of the dual string model) in terms of a solution of a Riemann-Hilbert problem for a finite set of functions. We review the underlying QQ relations starting from simple spin chain examples, and describe the special features arising for AdS/CFT. We also discuss the recently found links between the Quantum Spectral Curve and the computation of correlation functions. To appear in a special issue of J Phys A based on lectures given at the Young Researchers Integrability School and Workshop 2018.

31 pages, 4 figures; v2: typos fixed

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Cited by in corpus (13)

• Integrable Deformations of Sigma Models
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Introduction to classical and quantum integrability
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Integrability treatment of AdS/CFT orbifolds
• Separation of variables for higher rank integrable models: review of recent progress
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve
• Hexagon Bootstrap in the Double Scaling Limit