Trace functions of the Parafermion vertex operator algebras

TL;DR

This paper studies the trace functions of Parafermion vertex operator algebras linked to simple Lie algebras and positive integers, deriving explicit formulas for their modular transformations.

Contribution

It provides explicit modular transformation formulas for trace functions of Parafermion vertex operator algebras associated with any finite-dimensional simple Lie algebra and positive integer levels.

Findings

Derived explicit modular transformation formulas

Analyzed trace functions for Parafermion VOAs

Extended understanding of VOA modular properties

Abstract

The trace functions for the Parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra $\g$ and any positive integer $k$ are studied and an explicit modular transformation formula of the trace functions is obtained.