Towards a Classification of Conformal Field Theories

Abstract

In order to make some sense out of the jungle of conformal field theories that have been discovered from string theory, physicists have tried to classify these vacuums using various techniques, with varying degrees of success. At present, no comprehensive classification scheme exists that gives us insight into the structure of these vacuums. In fact, it is still largely a mystery why conformal field theories behave as they do. There has been some progress in understanding conformal field theories with finite numbers of primary fields, but there is almost no real understanding of conformal field theories with infinite numbers of primary fields. If a convenient and powerful classification scheme could be devised, then it may be possible to see nontrivial relationships between different conformal field theories, which in turn may help us to understand which, if any, of these conformal field theories have a physical application.