Ghost Systems: A Vertex Algebra Point of View

TL;DR

This paper explores fermionic and bosonic ghost systems through vertex algebras, revealing their conformal structures, symmetries, and invariant subalgebras, and providing methods to compute character formulas for twisted modules.

Contribution

It introduces a unified vertex algebra framework for ghost systems, relates their conformal structures, and analyzes invariant subalgebras, especially Z_N-invariant ones, from a W-algebra perspective.

Findings

Derived character formulas for twisted modules

Identified and studied Z_N-invariant subalgebras

Established relationships between conformal structures

Abstract

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a W-algebra point of view with particular emphasis on Z_N-invariant subalgebras of the fermionic ghost system.