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

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.

17 pages, one figure; v2: added refs and rewrote a little of the parabolic subalgebra discussion in Sec. 3 (no change to results); v3: added a sketch proof of Prop. 1, several clarifications and a few more refs (again, no change to results)

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