Chiral conformal field theory
Course notes
Intro
video1 [15min] (different notions of CFT)
Riemann surfaces with boundary
video2 [18min] (complex cobordisms)
video3 [37min] (conformal welding)
video4 [29min] (cobordisms with thin parts)
video5 [35min] (moduli of cobordisms)
Definition of chiral CFT
video6 [30min] (full vs chiral CFT)
video7 [13min] (algebras of observables)
video8 [34min] (disjoint union and tensor product)
video9 [18min] (the vacuum sector)
video10 [29min] (the fusion product)
Central extensions
video11 [21min] (central extensions of the semigroup of annuli)
video12 [37min] (the Virasoro algebra)
video13 [49min] (the cohomology of the Witt algebra)
video14 [39min] (the holomorphicity condition)
video15 [51min] (Ann(S¹) as complexification of Diff(S¹))
video16 [37min] (integrating the Virasoro cocycle)
Examples of chiral CFTs
video17 [32min] (loop groups)
video18 [25min] (minimal & WZW models)
video19 [36min] (spin CFTs)
video20 [36min] (the chiral free fermion CFT)
video21 [21min] (functors associated to cobordisms)
The positive energy condition
video22 [40min] (trace class maps and the positive energy condition)
video23 [16min] (thick cobordisms and trace class maps)
video24 [44min] (trivializing the annulus functors)
Representation theory
video25 [37min] (representations of Virasoro)
video26 [23min] (structure of finite dimensional simple Lie algebras)
video27 [30min] (representations of finite dimensional simple Lie algebras)
video28 [51min] (affine Lie algebras)
video29 [68min] (the Sugawara construction)
video30 [61min] (the Sugawara construction - proofs)
Fields