Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve

Abstract

This review is based on the lectures given by the author at the Les Houches Summer School 2016. It describes the recently developed Quantum Spectral Curve (QSC) for a non-perturbative planar spectrum of N=4 Super Yang-Mills theory in a pedagogical way starting from the harmonic oscillator and avoiding a long historical path. We give many examples and provide exercises. At the end we give a list of the recent and possible future applications of the QSC.

References in corpus (7)

• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• One-point Functions in AdS/dCFT from Matrix Product States
• Asymptotic one-point functions in AdS/dCFT
• Strong Coupling Expansion for the Conformal Pomeron/Odderon Trajectories
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The spectrum of tachyons in AdS/CFT

Cited by in corpus (30)

• Strongly γ-deformed N=4 SYM as an integrable CFT
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• N=2 Conformal SYM theories at large N
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Introduction to classical and quantum integrability
• A review of the AdS/CFT Quantum Spectral Curve
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Critical loop models are exactly solvable
• Integrable spin chains and cellular automata with medium range interaction
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Integrability treatment of AdS/CFT orbifolds
• On analytical perturbative solution of ABJM quantum spectral curve
• On type 0 string theory in solvable RR backgrounds
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• NNNLLA BFKL pomeron eigenvalue in the planar N=4 SYM theory
• Loop equations for generalised eigenvalue models
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• Novel aspects of integrability for NLSMs in symmetric spaces
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve