Quantum topology/algebra seminar

Event Date: 

Thursday, January 19, 2017 - 11:00am to 12:00pm

Event Location: 

  • 6635 South Hall
Speaker: James Tener
 
Title: On classification of conformal field theories by their representation category
 
Abstract: By work of Huang and Lepowsky, the category of representations of a rational vertex operator algebra is a modular tensor category, but this category alone does not contain all of the information of the VOA. Motivated by the goal of simulating a conformal field theory on a quantum computer, one can ask what additional data, beyond that of a modular tensor category, is needed to recover the VOA. 
 
In this talk I will present joint work with Zhenghan Wang in which we explore the answer to this question when the modular tensor category has two or three simple objects. In particular, we introduce a class of "extremal" vertex operator algebras V, and under the assumption that Rep(V) has two or three simple objects, we prove that the characters of the theory can be recovered from the category Rep(V) along with two additional choices of positive numbers. Our main technique is the theory of vector valued modular forms, as developed in this context by Bantay and Gannon.
 
No particular background in vertex operator algebras will be assumed.