Quantum integrability and functional equations

Abstract

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

PhD thesis. Contains also unpublished previously results and introduction to the subject of integrability in terms of functional equations. 210 pages+references; v2: references added, typos corrected

References in corpus (76)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• NLO vector-boson production matched with shower in POWHEG
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• 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
• Quantum corrections to the string Bethe ansatz
• Spinning strings and AdS/CFT duality
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Light Meson Physics from Maximally Twisted Mass Lattice QCD
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• String hypothesis for the AdS_5 x S^5 mirror
• On AdS_5 x S^5 String S-matrix
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• On the highest transcendentality in N=4 SUSY
• On the Singularities of the Magnon S-matrix
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Measurement of the W -> lnu and Z/gamma* -> ll production cross sections in proton-proton collisions at sqrt(s) = 7 TeV with the ATLAS detector
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Five loop Konishi from AdS/CFT
• On the Hopf algebra structure of the AdS/CFT S-matrix
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• Five-loop Konishi from the Mirror TBA
• Complete 1-loop test of AdS/CFT
• Sweet Spot Supersymmetry
• A Universality Test of the Quantum String Bethe Ansatz
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• The Dressing Factor and Crossing Equations
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1|s+1)
• Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator
• Strong coupling limit of Bethe Ansatz equations
• Solution to the Ward Identities for Superamplitudes
• On the SU(2|1) WZW model and its statistical mechanics applications
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• The Four-Loop Dressing Phase of N=4 SYM
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Constructing the AdS/CFT dressing factor
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Strings as Multi-Particle States of Quantum Sigma-Models
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• From Characters to Quantum (Super)Spin Chains via Fusion
• Scaling function in AdS/CFT from the O(6) sigma model
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Asymptotic Bethe Ansatz from String Sigma Model on S^3 x R
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models
• Integrable twists in AdS/CFT
• NGN, QCD_2 and chiral phase transition from string theory
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• $w_{\infty }$ 3-algebra
• Nonperturbative scales in AdS/CFT
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• Discrete Hirota dynamics for AdS/CFT
• Coordinate Bethe Ansatz for the String S-Matrix
• Quantum Stability for the Heisenberg Ferromagnet
• How Well Does AdS/QCD Describe QCD?
• Spiky Strings and Spin Chains
• Strong coupling expansion of Baxter equation in N=4 SYM
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Aspects of Integrability in AdS/CFT Duality
• The 2-loop generalized scaling function from the BES/FRS equation
• Current Algebra and Integrability of Principal Chiral Model on the World-sheet with General Metric
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)

Cited by in corpus (33)

• Review of AdS/CFT Integrability: An Overview
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• Exciting the GKP string at any coupling
• Solving the AdS/CFT Y-system
• Lectures on the Bethe Ansatz
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Yangians, S-matrices and AdS/CFT
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Renormalons in integrable field theories
• Resurgence in the O(4) sigma model
• New renormalons from analytic trans-series
• Resurgence for superconductors
• Exact perturbative results for the Lieb-Liniger and Gaudin-Yang models
• From perturbative to non-perturbative in the O(4) sigma model
• Testing the Bethe ansatz with large N renormalons
• Hybrid NLIE for the Mirror AdS_5 x S^5
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• A review of the AdS/CFT Quantum Spectral Curve
• Analytic resurgence in the O(4) model
• Resurgence and renormalons in the one-dimensional Hubbard model
• Instanton effects vs resurgence in the $O(3)$ sigma model
• Analytical results for the capacitance of a circular plate capacitor
• More about "short" spinning quantum strings
• Resurgence in the Bi-Yang-Baxter Model
• Instantons, renormalons and the theta angle in integrable sigma models
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor
• Three roads to the energy gap
• Asymptotics in an Asymptotic CFT
• Integrable systems and AdS/CFT duality
• Resurgence and $1/N$ Expansion in Integrable Field Theories
• Asymptotics in the bi-Yang-Baxter Sigma Model