by P Bouwknegt (University of Southern California) & K Schoutens (Princeton University)

Table of Contents (140k)
Preface (76k)
Introductory Chapters (586k)
History and Background (3,645k)

W-symmetry is an extension of conformal symmetry in two dimensions. Since its introduction in 1985, W-symmetry has become one of the central notions in the study of two-dimensional conformal field theory. The mathematical structures that underlie W-symmetry are so-called W-algebras, which are higher-spin extensions of the Virasoro algebra. This book contains a collection of papers on W-symmetry, covering the period from 1985 through 1993. Its main focus is the construction of W-algebras and their representation theory. A recurrent theme is the intimate connection between W-algebras and affine Lie algebras. Some of the applications, in particular W-gravity, are also covered.

The significance of this reprint volume is that there are no textbooks entirely devoted to the subject.

• History and Background
• Classical W-Algebras and Their Connection to Toda Field Theories
• Quantum W-Algebras
• Quantum Drinfel'd-Sokolov Reduction
• Coset Constructions
• W_∞ Type Algebras
• W-Gravity and W-Strings