Vertex Operator Algebras

Michaelmas Term 2017
Fridays 14.30-16.00 (weeks 2-4 and 6-8)
C2 Andrew Wiles Building

Lecturer: Prof. Christopher Beem

Prerequisites

Some familiarity with quantum field theory is useful, but is not technically necessary.

Course description

This is a nine-hour (six times 1.5 hours) lecture course covering the basics of vertex operator algebras. The rough outline is as follows:

• Lecture 1 - Definition of a vertex operator algebra; locality; commutative vertex algebras.
• Lecture 2 - The Heisenberg vertex operator algebra; normal ordering; Dong's lemma.
• Lecture 3 - VOA examples: symplectic bosons, Virasoro VOA, affine Kac-Moody VOA; operator product expansion.
• Lecture 4 - Redefining VOAs with the OPE; associativity and bootstrapping VOAs.
• Lecture 5 - New VOAs from old: tensor products, vertex operator subalgebras, VOA quotients, coset VOAs, cohomological constructions.
• Lecture 6 - Drinfel'd-Sokolov reduction.

Coursework

There is no coursework for this course.

References

• E. Frenkel and D. Ben-Zvi - Vertex Algebras and Algebraic Curves
• V. Kac - Vertex Algebras for Beginners
• P. Bouwknegt and K. Schoutens - W-Symmetry in Conformal Field Theory

Class Information

There will be no classes given for this course.