Two-dimensional conformal field theory and beyond. Lessons from a continuing fashion.

DOI10.1023/A:1010882404019zbMATH Open1036.81040arXivmath-ph/0011014MaRDI QIDQ5945518

Publication date: 2001

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Abstract: Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the subject we emphasize the role of CFT in bridging the gap between mathematics and quantum field theory and discuss some new physical concepts that emerged in the study of CFT models: anomalous dimensions, rational CFT, braid group statistics. In an aside, at the end of the paper, we share the misgivings, recently expressed by Penrose, about some dominant trends in fundamental theoretical physics.

Full work available at URL: https://arxiv.org/abs/math-ph/0011014

zbMATH Keywords

anomalous dimension braid statistics, operator product expansions current algebras rational conformal field theory

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Axiomatic quantum field theory; operator algebras (81T05) Applications of functional analysis in quantum physics (46N50)