The classification of semi-conformal structures of Heisenberg vertex operator algebras

This paper aims to understand Heisenberg vertex algebras in terms of their semi-conformal structures. First, we study the moduli space of conformal and semi-conformal structures on Heisenberg vertex algebras that have the standard fixed conformal gradation by describing their automorphism groups. We describe its semi-conformal vectors as pairs consisting of regular subspaces and the projections of a fixed vector space in these regular subspaces. Then by automorphism groups G of Heisenberg vertex operator algebras, we get all G-orbits of varieties of their semi-conformal vectors and give some characterizations of Heisenberg vertex operator algebras.