Bosonic Ghosts at c=2 as a Logarithmic CFT

作者：Ridout David^*; Wood Simon

来源：Letters in Mathematical Physics, 2015, 105(2): 279-307.

DOI：10.1007/s11005-014-0740-z

• Logarithmic conformal field theory
• vertex algebras
• modular transformations
• fusion

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.

• 出版日期2015-2