Integrable systems and AdS/CFT duality

Abstract

This PhD thesis explores the similarities between integrable spin chains and quantum field theories, such as Super Yang Mills. We first study integrable spin chains and build explicitly a polynomial "Backlund flow" and polynomial "Q-operators", which allow to diagonalize the Hamiltonian. We then study integrable field theories et show how to obtain "Q-functions", analogous to the Q-operators built for spin chains. It turns out that several important informations are contained in the analytic properties of these Q -functions. That allows to obtain, in the framework of the thermodynamic Bethe ansatz, a finite number of non-linear integral equations encoding the finite-size spectrum of the theory which we study. This system of equations is equivalent to an infinite system of equations, known as "Y-system", which had been quite recently conjectured in the case of the AdS/CFT duality.

PhD thesis : 275 pages, including 10 introductory pages in french at the begining (repeated afterwards in english) v2 : typos fixed and five references added

References in corpus (20)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• A Shortcut to the Q-Operator
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Wrapping interactions at strong coupling -- the giant magnon
• Baxter Q-Operators and Representations of Yangians
• Baxter's Q-operators for supersymmetric spin chains
• Complete 1-loop test of AdS/CFT
• Solving the AdS/CFT Y-system
• Wronskian Solution for AdS/CFT Y-system
• Konishi operator at intermediate coupling
• Classical tau-function for quantum spin chains
• From Characters to Quantum (Super)Spin Chains via Fusion
• Finite-size effects in the superconformal beta-deformed N=4 SYM
• The Baxter's Q-operator for the W-algebra $W_N$
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators
• Unified approach to the SU(2) Principal Chiral Field model at Finite Volume

Cited by in corpus (3)

• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Integrability of the AdS_5 x S^5 superstring and its deformations
• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains