Two-dimensional conformal field theory can be built entirely from its chiral symmetry algebra: the observables span an infinite-dimensional graded Lie algebra containing the Virasoro algebra, whose unitary irreducible highest weight modules are the sectors of the theory. The same triangular-decomposition machinery, applied to affine Kac-Moody algebras realised as centrally extended loop algebras, yields WZW theories with Sugawara Virasoro generators and coset theories built from differences of Virasoro algebras. A student learns to move between the physical objects (operator products, correlation functions, fusion rules, modular invariants) and the algebraic ones (highest weights, levels, Weyl-Kac characters, S-matrices).
Four lectures by Jurgen Fuchs (DESY; 59 pages, extended from the August 1996 Budapest graduate course, for Springer Lecture Notes in Physics). Lecture 1 builds two-dimensional conformal field theory …