Teaching

Conformal Field Theory

Goal: Introduce the basics of conformal field theory and construct the corresponding formalism for minimal models (including the relation to matrix models) and WZW models.

Syllabus:

Conformal Symmetry: Phase transitions and scale invariance; Conformal group, Virasoro algebra, OPE's and Ward identities; Superconformal symmetry, RNS algebras and spin fields.

Operator Formalism: Free fields, conformal families and bootstrap; Bosons and fermions on the torus, modular invariance, CFT and Riemann surfaces; Boundary conditions and Verlinde formula.

Minimal Models: Verma modules, representations and Kac determinant; Minimal models, unitarity and fusion rules; Coulomb gas formalism; Modular invariance.

Matrix Models: The 1/N expansion, semi-classical approximation, resolvent and spectral curve; Orthogonal polynomials and correlation functions; Critical points and DSL; Non-perturbative phenomena.

Current Algebras and WZW Models: Simple Lie algebras and affine Lie algebras; WZW models, Sugawara construction and Knizhnik-Zamolodchikov equation; Ishibashi states.