Bosonic Ghosts at $c=2$ as a Logarithmic CFT

TL;DR

This paper explores the logarithmic conformal field theory of bosonic ghosts at central charge c=2, deriving modular properties, fusion coefficients, and invariant partition functions using a new formalism.

Contribution

It introduces a novel formalism for logarithmic CFTs applied to bosonic ghosts, including parabolic Verma modules and explicit modular and fusion results.

Findings

Derived S-transformation formulae for characters

Obtained non-negative integer Verlinde coefficients

Constructed modular invariant partition functions

Abstract

Motivated by Wakimoto free field realisations, the bosonic ghost system of central charge $c=2$ is studied using a recently proposed formalism for logarithmic conformal field theories. This formalism addresses the modular properties of the theory with the aim being to determine the (Grothendieck) fusion coefficients from a variant of the Verlinde formula. The key insight, in the case of bosonic ghosts, is to introduce a family of parabolic Verma modules which dominate the spectrum of the theory. The results include S-transformation formulae for characters, non-negative integer Verlinde coefficients, and a family of modular invariant partition functions. The logarithmic nature of the corresponding ghost theories is explicitly verified using the Nahm-Gaberdiel-Kausch fusion algorithm.