Vertex Operator Algebras in Mathematics and Physics

by Berman, Stephen; Billig, Yuly; Huang, Yi-Zhi; Lepowsky, James

• ISBN13: 9780821828564
• ISBN10: 0821828568
• Format: Hardcover
• Copyright: 2003-11-01
• Publisher: Amer Mathematical Society

Summary

Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.

Table of Contents

Preface	p. vii
Schedule of Talks	p. xi
Finiteness of Conformal Blocks Over the Projective Line	p. 1
Permutation Orbifolds and their Applications	p. 13
Category Theory for Conformal Boundary Conditions	p. 25
GNAVOA, I. Studies in Groups, Nonassociative Algebras and Vertex Operator Algebras	p. 71
Genera of Vertex Operator Algebras and Three-dimensional Topological Quantum Field Theories	p. 89
Riemann Surfaces with Boundaries and the Theory of Vertex Operator Algebras	p. 109
Vertex (Operator) Algebras are "Algebras" of Vertex Operators	p. 127
Correlation Functions, Differential Operators and Vertex Operator Algebras	p. 139
Relations for Annihilating Fields of Standard Modules for Affine Lie Algebras	p. 169
From Branes to Boundary Conformal Field Theory: Draft of a Dictionary	p. 189
Open Strings and Non-commutative Geometry	p. 227
The World Sheet Revisited	p. 241
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