Towards the Construction of Local Logarithmic Conformal Field Theories

TL;DR

This paper develops methods to construct local non-chiral logarithmic conformal field theories from chiral components, addressing the challenge of non-factorization and locality in LCFTs.

Contribution

It introduces two methods for building local representations from chiral Jordan cells and explores assembling non-chiral correlators, advancing the understanding of LCFT locality.

Findings

Methods for constructing local representations from chiral Jordan cells.

Framework for assembling non-chiral correlation functions.

Analysis of locality constraints in LCFTs.

Abstract

Although logarithmic conformal field theories (LCFTs) are known not to factorise many previous findings have only been formulated on their chiral halves. Making only mild and rather general assumptions on the structure of an chiral LCFT we deduce statements about its local non-chiral equivalent. Two methods are presented how to construct local representations as subrepresentations of the tensor product of chiral and anti-chiral Jordan cells. Furthermore we explore the assembly of generic non-chiral correlation functions from generic chiral and anti-chiral correlators. The constraint of locality is studied and the generality of our method is discussed.