Introduction to Vertex algebras

Fall 2011, IMPA
Instructor: Reimundo Heluani
Office: 432
Tuesdays and Fridays 15:30-17:00 Sala 347


Aula 1 18/3
Motivations: CFTs and representations of certain infinite dimensional Lie algebras. Formal distributions. Delta distributions. Locality.
Aula 2 22/3
Local distributions of two variables. Decomposition Theorem for local distributions. Formal Fourier transform. Formal distribution Lie superalgebras.
Aula 3 25/3
Properties of the Formal Fourier transform. Lambda brackets. Conformal Lie algebras. Relation to formal distribution Lie algebras. Examples.
Aula 4 28/3
Examples of Conformal Lie algebras and superalgebras. Affine Kac-Moody. Virasoro. N=1 or Neveu Schwarz, N=2. Relations to Lie algebras of vector fields on supercurves.
Aula 5 1/4
More on Examples N=2. Topological Twist. N=4. Definition of Poisson vertex algebras. Normally ordered product.
Aula 6 5/4
Properties of the normally ordered product. Sesquilinearity. Relation with the derivative for conformal algebras. Leibniz rule (non commutative Wick formula). Quasi-commutativity.
Aula 7 8/4
Definition of vertex algebras. Dong's lemma. Universal enveloping vertex algebra. Super-fermions. Bosonization. Sugawara construction.
Aula 8 12/4
Sugawara construction continuation.
Aula 9 15/4
Boson-Fermion correspondence. Charge, energy. State-field correspondence.
Aula 10 19/4
Uniqueness. n-th product theorem.