TITLE: Simple current extensions in VOA theory and CFTs
QUESTION [6 upvotes]: I apologize in advance if this is too broad and off-topic here. I have seen some papers in the field of vertex operator algebras (VOA) theory about simple current extensions. As far as I understand simple currents are invertible objects in some vertex tensor category (for example representation categories of certain VOAs). I am trying to get an overview of why these are important. 

How did simple current extensions appear in conformal field theory (CFT) and why are they important in physics?
What role do they play in VOA theory ?
What are some good references on this topic?

REPLY [3 votes]: Regarding your first question, physicists are interested in classifying modular invariant partition functions for two-dimensional rational conformal field theories. Simple currents are a useful tool for constructing such partition functions. An early physics paper on the subject that develops this point of view is https://www.sciencedirect.com/science/article/abs/pii/0370269389909489?via%3Dihub
Furthermore, this paper also introduced the name "simple current".