Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin

Abstract

These lectures give a basic introduction to $\mathcal{N}=4$ SYM theory and the integrability of its planar spectral problem as seen from the perspective of a recent development, namely the application of integrability techniques in the study of one-point functions in a defect version of the theory.

arXiv comment45 pages, 5 figures, based on lectures given at the Les Houches Summer School "Integrability: From Statistical Systems to Gauge Theory," 2016

References in corpus (48)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Holography and Defect Conformal Field Theories
• The su(2|3) Dynamic Spin Chain
• The Bootstrap Program for Boundary CFT_d
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• The Noncommutative Bion Core
• Tailoring Three-Point Functions and Integrability
• Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects
• Form factors at strong coupling via a Y-system
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• One-point Functions in Defect CFT and Integrability
• A Shortcut to the Q-Operator
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• One-point Functions in AdS/dCFT from Matrix Product States
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Transport Properties of Holographic Defects
• AdS/dCFT one-point functions of the SU(3) sector
• Notes on adding D6 branes wrapping RP3 in AdS4 x CP3
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Nonplanar Integrability
• A note on the holography of Chern-Simons matter theories with flavour
• The Four-Loop Dressing Phase of N=4 SYM
• Structure constants at wrapping order
• One-loop one-point functions in gauge-gravity dualities with defects
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• Asymptotic one-point functions in AdS/dCFT
• Overlaps of $q$-raised Néel states with XXZ Bethe states and their relation to the Lieb-Liniger Bose gas
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Overlaps of Partial Neel States and Bethe States
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Holographic Interface-Particle Potential
• Expectation values of chiral primary operators in holographic interface CFT
• Adding Flavor to AdS4/CFT3
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• The Hagedorn temperature of AdS5/CFT4 via integrability
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• One-loop Wilson loops and the particle-interface potential in AdS/dCFT
• Asymptotic Four Point Functions
• Circular Wilson loops in defect Conformal Field Theory
• Two-point functions of SU(2)-subsector and length-two operators in dCFT

Cited by in corpus (8)

• Scalar one-point functions and matrix product states of AdS/dCFT
• Universality at large transverse spin in defect CFT
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Introduction to classical and quantum integrability
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• String integrability of the ABJM defect
• A non-integrable quench from AdS/dCFT
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM