C-Graded Vertex Algebras and Conformal Flow
Abstract
We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by 'lowest weight vectors'. We show that such vertex algebras have a 'good' representation theory in the sense that there is a Zhu algebra A(V) and a bijection between simple admissible V-modules and simple A(V)-modules. We also consider pseudo vertex operator algebras, which are C-graded vertex algebras with a conformal vector such that the homogeneous subspaces of V are generalized eigenspaces for L(0); essentially, these are VOAs that lack any semisimplicity or integrality assumptions on L(0). As a motivating example, we show that deformation of the conformal structure (conformal flow) of a strongly regular VOA (eg a lattice theory, or WZW model) is a path in a space whose points are PVOAs.
Cite
@article{arxiv.1308.0557,
title = {C-Graded Vertex Algebras and Conformal Flow},
author = {Rob Laber and Geoffrey Mason},
journal= {arXiv preprint arXiv:1308.0557},
year = {2015}
}