Non-Chiral Logarithmic Couplings for the Virasoro Algebra

TL;DR

This paper explores non-chiral staggered Virasoro modules to explain unusual logarithmic couplings in c=0 bulk conformal field theories, proposing a natural family of modules and conjecturing values for non-chiral couplings.

Contribution

It introduces non-chiral staggered Virasoro modules and explains non-standard logarithmic couplings through a natural family of bulk modules.

Findings

Identifies a unique non-standard logarithmic coupling consistent with structure.

Shows the persistence of this coupling for general central charges.

Proposes a conjecture for non-chiral logarithmic coupling values.

Abstract

This Letter 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 two zero-modes acting non-semisimply. This is motivated by the "puzzle" recently reported in arXiv:1110.1327 [math-ph] 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.