Logarithmic Conformal Field Theories via Logarithmic Deformations

TL;DR

This paper introduces a method to construct logarithmic conformal field theories by deforming and extending ordinary CFTs, covering models like Virasoro minimal models and WZW theories.

Contribution

It presents a novel two-step construction for generating logarithmic CFTs from existing theories through algebraic deformations and extensions.

Findings

Constructs logarithmic CFTs from ordinary CFTs using algebraic deformations.

Applies the method to (2,p) Virasoro models and sl(2) WZW theory.

Demonstrates the emergence of fermionic operators via Clifford algebra extensions.

Abstract

We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra representation on V\tensor End K[[z,1/z]], where K is an auxiliary finite-dimensional vector space, and ii) extending C by operators corresponding to the endomorphisms End K. For K=C^2, with End K being the two-dimensional Clifford algebra, our construction results in extending C by an operator that can be thought of as \partial^{-1}E, where \oint E is a fermionic screening. This covers the (2,p) Virasoro minimal models as well as the sl(2) WZW theory.