Bosonic Ghosts at \(c=2\) as a Logarithmic CFT

Analyses the \(c=2\) bosonic ghost system, a building block of many free field realisations, as a logarithmic conformal field theory using the standard module formalism. Derives the modular transformations of characters, non-negative integer Verlinde coefficients and infinitely many modular invariant partition functions, with explicit fusion computations confirming that the theory is logarithmic.

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.

Recommended citation: D. Ridout, and S. Wood, Lett. Math. Phys. 105, 279–307, (2015)
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