Speaker：Yizhi Huang (Rutgers University)

Time：2023-6-15, 16:30

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

I will discuss a proof of a conjecture of almost twenty years on the modular invariance of (logarithmic) intertwining operators. Let V be a C_2-cofinite vertex operator algebra without nonzero elements of negative weights. The conjecture states that the vector space spanned by pseudo-q-traces shifted by -c/24 of products of (logarithmic) intertwining operators among grading-restricted generalized V-modules is a module for the modular group SL(2, Z). In 2015, Fiordalisi proved that such pseudo-q-traces are absolutely convergent and have the genus-one associativity property and some other properties. Recently, I have proved this conjecture completely. This modular invariance result gives a construction of C_2-cofinite genus-one logarithmic conformal field theories. We expect that it will play an important role in the study of several conjectures on C_2-cofinite logarithmic conformal field theories, including, in particular, the rigidity and modularity of the corresponding braided tensor categories.