Learning Seminar on the Wess-Zumino-Witten Model

(Suggestions welcome!)

2D Conformal field theory

Segal’s manuscript, see also Pressley-Segal for some omitted proofs
For physics aficionados: Knizhnik-Zamolodchikov

Representation theory

Affine Lie algebras: Kac
Twisted D-modules: Beilinson-Bernstein

Conformal blocks/KZ connection

Original: Tsuchiya-Ueno-Yamada
Contruction via localization: Beilinson-Schechtman
Solving KZ in genus 0: Schechtman-Varchenko

Other ways to think about conformal blocks

Nonabelian theta functions: Beauville-Laszlo
Chiral homology: Beilinson-Drinfeld (for the brave!)
Vertex algebras: Frenkel-Ben-Zvi
Recent survey on open problems

3-manifolds/TQFT/Quantum groups

For the creative minds: Witten
There’s also Kazhdan-Lusztig, but I’m hoping not to go in that direction


Via Hodge theory: Ramadas (genus 0, SL2), Belkale (genus 0, any G), Looijenga’s genus 0 and higher genus proposal
Via differential cohomology: Brylinski-McLaughlin’s Duke I, Duke II, Kostant volume


Motivic meaning of the “level”: Brylinski-Deligne
Notes on Quantum Langlands from 2007. There’s by now a vast amount of literature: ask me if you are interested!