A Collection of Exercises in Two-Dimensional Physics, Part 1
arXiv:hep-th/0003190
Abstract
This document is an introduction to and review of two-dimensional mathematical physics. The reader is introduced to the subject matter primarily through problems, which are presented along with detailed worked solutions. For each chapter, there is a brief summary of important results and ideas that precedes the problems and the solutions. This document can be worked through independently by one wishing to learn this subject; alternatively, this could serve as a companion to a more conventional review article or textbook on the subject. The current release contains Part I, and includes six chapters: 1. Curiosities In 2 Dimensions 2. General Principles Of Conformal Field Theory 3. Correlators In Critical Models 4. Other Models In Conformal Field Theory 5. Construction Of New Models 6. Modular Invariance
Release 1.0; Latex file, several additional packages are used; 233 pages; figures included as eps files; cross-references to the second part may be currently incorrect. Part II will be forthcoming later this year.
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- Dirichlet-Branes and Ramond-Ramond Charges
- 2D Gravity and Random Matrices
- Implications of Conformal Invariance in Field Theories for General Dimensions
- Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
- String Theory on Calabi-Yau Manifolds
- On the quantum inverse scattering problem
- Quantum Solitons in Affine Toda Field Theories
- Planar Duality in WZW Models
- Quantum Inverse Scattering Method. Selected Topics
- Affine Toda field theory on a half line
- Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
- Exact S-Matrices for Nonsimply-Laced Affine Toda Theories
- Multi-point Local Height Probabilities in the Integrable RSOS Model
- Bosonization and QCD in Two Dimensions
- Conformal Field Theory Techniques in Random Matrix models
- The resolution of field identification fixed points in diagonal coset theories
- ON GRAVITATIONAL DRESSING OF 2D FIELD THEORIES IN CHIRAL GAUGE
- On a generalised bootstrap principle
- Lectures on Orientifolds and Duality
- Solvable lattice models labelled by Dynkin diagrams
- From CFT's to Graphs
- Duality in Quantum Toda theory and W-algebras
- On the construction of integrable dilute ADE models
- Null vectors of the W_3 algebra
- Completeness of boundary conditions for the critical three-state Potts model
- Unifying W-Algebras
- Bosonization of ZF Algebras: Direction Toward Deformed Virasoro Algebra
- Analytic Expressions for Singular Vectors of the Superconformal Algebra
- The Classification of SU(3) Modular Invariants Revisited
- Orbifold analysis of broken bulk symmetries
- Nonlinear Integral Equation and Finite Volume Spectrum of Minimal Models Perturbed by
- A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models
- Algebra of screening operators for the deformed algebra
- Quantum integrability in two-dimensional systems with boundary
- Fusion of \ade Lattice Models
- Monstrous moonshine and the classification of CFT
- Symmetry breaking boundary conditions and WZW orbifolds
- Hidden geometrical structures in integrable models
- Fusion in the W_3 algebra
- Single Particle Excitations in the Lattice E_8 Ising Model
- A new approach to the correlation functions of W-algebras
- Beyond CFT : Deformed Virasoro and Elliptic Algebras
- Introduction to Quantum Lie Algebras
- An introduction to quantum groups and non-commutative differential calculus
- Factorization and q-Deformed Algebra of Quantum Anharmonic Oscillator
- From factorizable S-matrices to conformal invariance