Title: A unitary tensor product theory for unitary vertex operator algebra modules
Abstract: A modular tensor category (MTC) structure for 2d rational conformal field theory was found in physics by Moore-Seiberg, and was proved mathematically by Huang-Lepowsky using the language of vertex operator algebras (VOAs). However, it is unclear whether this MTC has a unitary structure. In this talk, I will define an inner product on the tensor product of two unitary representations of a unitary rational VOA, under which the MTC becomes unitary.