# Vertex Operator Algebras in Mathematics and Physics

Share this page *Edited by *
*Stephen Berman; Yuly Billig; Yi-Zhi Huang; James Lepowsky*

A co-publication of the AMS and Fields Institute

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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

Graduate students and researchers 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

## Vertex Operator Algebras in Mathematics and Physics

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Schedule of talks xi12
- Finiteness of conformal blocks over the projective line 114
- Permutation orbifolds and their applications 1326
- Category theory for conformal boundary conditions 2538
- GNAVOA, I. Studies in groups, nonassociative algebras and vertex operator algebras 7184
- Genera of vertex operator algebras and three-dimensional topological quantum field theories 89102
- Riemann surfaces with boundaries and the theory of vertex operator algebras 109122
- Vertex (operator) algebras are “algebras” of vertex operators 127140
- Correlation functions, differential operators and vertex operator algebras 139152
- Relations for annihilating fields of standard modules for affine Lie algebras 169182
- From branes to boundary conformal field theory: Draft of a dictionary 189202
- Open strings and non-commutative geometry 227240
- The world sheet revisited 241254
- Back Cover Back Cover1265