Conformal field theory
A. In two dimensions:
1. Introductory
The original papers
Belavin, Polyakov and Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory
Zamolodchikov and Zamolodchikov, Conformal field theory and critical phenomena in two-dimensional systems
Lecture notes
Dotsenko, Lectures on conformal field theory
Beilinson, Feigin, Mazur, Notes on conformal field theory
Ginsparg, Applied conformal field theory
Schellekens, Introduction to conformal field theory
Gaberdiel, An introduction to conformal field theory
Cardy, Conformal field theory and statistical mechanics
Jockers, Lecture notes on CFT
Litvinov, Lecture notes on CFT
Wendland, Snapshots of conformal field theory
Teschner, A guide to two-dimensional conformal field theory
Liniado, Two Dimensional Conformal Field Theory and a Primer to Chiral Algebras
Nawata, Tao, Yokoyama, Fudan lectures on 2d conformal field theory
Fuchs, Schweigert, Wood, Yang, Algebraic structures in two-dimensional conformal field theory
Books
Ketov, Conformal field theory
Henkel, Conformal Invariance and Critical Phenomena
Blumenhagen and Plauschinn, Introduction to conformal field theory
Polchinski, String theory, vol 1.
Fuchs, Affine Lie Algebras and Quantum Groups: an Introduction with applications in conformal field theory
2. Intermediate
Schottenloher, A mathematical introduction to conformal field theory
Gawedzki, Lectures on conformal field theory
Gawedzki, Conformal field theory
Gawedzki, Conformal field theory: a case study
Gannon, Monstrous moonshine and the classification of CFT
3. Advanced
Di Francesco, Mathieu, Senechal, Conformal field theory
Ueno, Conformal Field Theory with Gauge Symmetry
Etingof, Frenkel and Kirillov, Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
Kohno, Conformal field theory and topology
Huang et al (eds), Conformal Field Theories and Tensor Categories
Fuchs, Schweigert and Yang, String-Net Construction of RCFT Correlators
4. Special subjects
Boundary CFT
Runkel, Boundary problems in conformal field theory
Recknagel and Schomerus, Boundary Conformal Field Theory and the Worldsheet Approach to D-Branes
CFT with defects
...
Connnections to integrable systems
Bazhanov, Lukyanov, Zamolodchikov, Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz
...
4. Mathematical foundations
Tener, Representation theory in chiral conformal field theory: from fields to observables
Through modular functors
Segal, The definition of conformal field theory
Segal, Two-dimensional conformal field theories and modular functors
Through vertex operator algebras and full field algebras
Huang, Geometric interpretation of vertex operator algebras
Huang, Vertex operator algebras and the Verlinde conjecture
Huang, Vertex operator algebra, the Verlinde conjecture and modular tensor categories
Huang and Kong, Full field algebras
Kong, Full field algebras, operads and tensor categories
Kong, Conformal field theory and a new geometry
Huang, Some open problems in mathematical two-dimensional conformal field theory
Through chiral algebras
Beilinson and Drinfeld, Chiral algebras
Gaitsgory, Notes on 2d conformal field theory and string theory
Through conformal nets
Longo, Conformal nets and intermediate subfactors
Bartels, Douglas, Henriques, Conformal nets and local field theory
Douglas and Henriques, Topological modular forms and conformal nets
Bartels, Douglas, Henriques, Conformal nets I: coordinate-free nets
Bartels, Douglas, Henriques, Conformal nets II: conformal blocks
Bartels, Douglas, Henriques, Conformal nets III: fusion of defects
Bartels, Douglas, Henriques, Conformal nets IV: the 3-category
Bartels, Douglas, Henriques, Conformal nets V: dualizability
Carpi et al, From Vertex Operator Algebras to Conformal Nets and Back
Carpi, Operator algebras and vertex operator algebras
Carpi, Gaudio, Hillier, From vertex operator superalgebras to graded-local conformal nets and back
Gui, Categorical extensions of conformal nets
Kawahigashi, Conformal Field Theory, Vertex Operator Algebras and Operator Algebras
Kawahigashi, Conformal Field Theory, Tensor Categories and Operator Algebras
Relevant mathematics:
- infinite-dimensional Lie (super)algebras
- vertex algebras
- associative algebras
- operads
- Riemann surfaces
- some operator theory and theory of distributions
- quantum groups
- some category theory
B. In higher dimensions:
Luscher and Mack, Global conformal invariance in quantum field theory
Fradkin and Palchik, Conformal Quantum Field Theory in D-dimensions
Rychkov, EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions
Evans, Miller, Russel, A conformal field theory primer in D ≥ 3