Free Field Realisations of Staggered Modules in 2D Logarithmic CFTs

TL;DR

This paper develops free field realizations of staggered modules in 2D logarithmic conformal field theories using bosonic Fock spaces, deriving a general formula for the β-invariant and providing explicit constructions.

Contribution

It introduces a general formula for the β-invariant of staggered Fock modules and constructs a broad class of these modules explicitly using free field methods.

Findings

Derived a formula for the β-invariant consistent with previous results.

Constructed explicit free-field models for many staggered modules.

Showed how to include weight-0 modes to generate these modules algebraically.

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.