An introduction to conformal field theory

A comprehensive introduction to two-dimensional conformal field theory is g iven. The structure of the meromorphic subtheory is described in detail, an d a number of examples are presented explicitly. Standard constructions suc h as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Z hu's algebra in classifying highest weight representations is elucidated. T he fusion product of two representations and the corresponding fusion rules are defined, and Verlinde's formula is explained. Finally, higher correlat ion functions are considered, and the polynomial relations of Moore and Sei berg and the quantum group structure of chiral conformal field theory are d iscussed. The treatment is relatively general and also allows for a descrip tion of less well known classes of theories such as logarithmic conformal f ield theories.