A review of the AdS/CFT Quantum Spectral Curve

TL;DR

This paper reviews the Quantum Spectral Curve framework in AdS/CFT, explaining its mathematical structure, underlying relations, and recent links to correlation function computations, providing a comprehensive introduction for researchers.

Contribution

It offers a detailed overview of the Quantum Spectral Curve in AdS/CFT, including foundational QQ relations and recent developments connecting it to correlation functions.

Findings

Clarified the QQ relations in integrability

Linked Quantum Spectral Curve to correlation functions

Provided educational overview for new researchers

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.