From Operator Algebras to Superconformal Field Theory

TL;DR

This paper reviews recent advances in the operator algebraic approach to superconformal field theory, covering representation theory, classifications, and connections to various mathematical structures.

Contribution

It synthesizes recent progress and highlights the interplay between operator algebras, supervertex operator algebras, Moonshine, and noncommutative geometry in superconformal field theory.

Findings

Summarizes classification results in superconformal field theory.

Explores relations between operator algebras and supervertex operator algebras.

Discusses connections to Moonshine and noncommutative geometry.

Abstract

We make a review on the recent progress in the operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory and noncommutative geometry.