Title: Representations of vertex operator algebras,
open-closed conformal field theories and string field theory

Abstract: For a vertex operator algebra V satisfying certain natural
positive-energy, reductivity and finiteness conditions, the category
of V-modules has been shown by me to have a natural modular tensor
category structure in the sense of Turaev. Open-closed conformal field
theories containing V have been shown by Kong and me in a series of
papers to be equivalent to pairs consisting of a noncommutative
Frobenius algebra and a commutative Frobenius algebra in suitable
modular tensor categories satisfying additional natural
conditions. This formulation and the corresponding construction of
open-closed conformal field theories provide a natural and general
framework for the study of string field theory. For example, Witten's
star product in open string field theory is nothing but the product
for noncommutative Frobenius algebras in the category of V-modules and
Witten's open string field action can be formulated and studied using
the representation theory of V.