BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

2001/11/30 by Michael Flohr · 11 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #cond-mat #hep-th

paper · pdf · doi:10.1142/s0217751x03016859

published as Int.J.Mod.Phys.A18:4497-4592,2003 · 91 pages, notes of lectures delivered at the first School and Workshop on Logarithmic Conformal Field Theory and its Applications, Tehran, September 2001. Amendments in Introduction

arxiv created 2002/06/06 · openalex publication_date 2003/10/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

Citations

• Logarithmic CFT on the Boundary and the World-Sheet
• Impulse Action on D-particles in Robertson-Walker Space Times, Higher-Order Logarithmic Conformal Algebras and Cosmological Horizons
• Gravitationally Dressed Conformal Field Theory and Emergence of Logarithmic Operators
• Curiosities at c=-2
• On the relation between integrability and infinite-dimensional algebras
• On Reducible but Indecomposable Representations of the Virasoro Algebra
• Logarithmic operators and dynamical extension of the symmetry group in the bosonic SU(2)0 and SUSY SU(2)2 WZNW models
• Infinite conformal symmetry in two-dimensional quantum field theory
• Logarithmic Yangians in WZW Models

Cited by

• Unitary truncations and critical gravity: a toy model
• Fusion algebras of logarithmic minimal models
• Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals
• The logarithmic triplet theory with boundary
• Two-Point Functions and Logarithmic Boundary Operators in Boundary Logarithmic Conformal Field Theories
• The origin of multiplets of chiral fields inSU(2)kat rational level
• The model in the limit (self-avoiding-walks) and logarithmic conformal field theory
• Magic in the spectra of the XXZ quantum chain with boundaries at Δ=0 and Δ=−1/2
• Boundary states in c=−2 logarithmic conformal field theory
• PP-waves and logarithmic conformal field theories
• Boundary states and symplectic fermions