Virasoro Algebra and Conformal Field Theory. 2019

1. Bootstrap in 2d CFT. Conformal algebra. Space of fields in CFT. Stress-energy-momentum tensor. Ward identities.
   
2. Virasoro algebra. Verma modules, Shapovalov form, singular vectors. Asymptotic behaviour of the Shapovalov form.
3. Conformal blocks . Vertex operators, conformal blocks. Zamolodchikov's recursion relations.
   
4. Degenerate fileds. Differential equation on conformal blocks, hypergeometric function, fusion rules. Three point functions.
   
5. Minimal models. Characters of representations. Unitarity.
6. Coset construction. Affine lie algebras. Coset construction. Unitary representations of the Virasoro algebra..
   
7. Drinfeld-Sokolov reduction. Finite dimensional case. Classical Drinfeld-Sokolov reduction. Quantum Drinfeld-Sokolov reduction.
   

Lecture notes and problems. (updated 01.11.2020)