Free Field Realisations of Staggered Modules in 2D Logarithmic CFTs

Abstract

We utilise bosonic Fock spaces, considered as Virasoro modules, to make free field realisations of the so-called staggered modules of two-dimensional logarithmic conformal field theories. A general formula for the $\beta$-invariant of a staggered Fock module is derived, and found to agree with values previously known in the literature. In this way a large class of staggered modules is produced; one which provides an explicit free-field construction for many of those previously studied. We show how these modules can arise algebraically by including the modes of weight-$0$ fields into the algebra.