Letters in Mathematical Physics

, Volume 105, Issue 2, pp 279–307 | Cite as

Bosonic Ghosts at c = 2 as a Logarithmic CFT

  • David RidoutEmail author
  • Simon Wood


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.

Mathematics Subject Classification

17B68 17B69 


Logarithmic conformal field theory vertex algebras modular transformations fusion 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Theoretical Physics, Research School of Physics and Engineering and Mathematical Sciences InstituteAustralian National UniversityActonAustralia
  2. 2.Department of Theoretical Physics, Research School of Physics and EngineeringAustralian National UniversityActonAustralia

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