TITLE: What do mathematicians currently do in conformal field theory (or more general field theory)
QUESTION [21 upvotes]: I am wondering what currently our mathematicians do related to conformal field theory, (I know currently it is a central topic, but I have only a vague idea what mathematicians do in there), or more generally topological field theory, field theory... I am extremely appreicated if there is any survey paper.

REPLY [3 votes]: If you are interested in operator algebras, try this review by Kawahigashi From Operator Algebras to Superconformal Field Theory, where connections to subfactor theory, moonshine and noncommutative geometry are pointed out.