Non-chiral logarithmic couplings for the Virasoro algebra

This paper initiates the study of what we call non-chiral staggered Virasoro modules, indecomposable modules on which two copies of the Virasoro algebra act with the zero-modes L ₀ and acting non-semisimply. This is motivated by the puzzle recently reported in Vasseur et al (2012 Phys. Rev. Lett. 108 161602) involving a non-standard measured value, meaning that the value is not familiar from chiral studies, for the b-parameter (logarithmic coupling) of a c = 0 bulk conformal field theory. Here, an explanation is proposed by introducing a natural family of bulk modules and showing that the only consistent, non-standard logarithmic coupling that is distinguished through structure is that which was measured. This observation is shown to persist for general central charges and a conjecture is made for the values of certain non-chiral logarithmic couplings.