Irrational Conformal Field Theory

Abstract

This is a review of irrational conformal field theory, which includes rational conformal field theory as a small subspace. Central topics of the review include the Virasoro master equation, its solutions and the dynamics of irrational conformal field theory. Discussion of the dynamics includes the generalized Knizhnik-Zamolodchikov equations on the sphere, the corresponding heat-like systems on the torus and the generic world- sheet action of irrational conformal field theory.Comment: 195 pages, Latex, 12 figures, to appear in Physics Reports. Typos corrected in Sections 13 and 14, and a footnote added in Section 1