What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT

Abstract

In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2,2p-1,2p-1,2p-1) series of triplet algebras and a bit logarithmic extensions of the minimal Virasoro models. Since in all known examples of logarithmic conformal field theories the vacuum representation of the maximally extended chiral symmetry algebra is an irreducible submodule of a larger, indecomposable module, its character provides a lot of non-trivial information about the theory such as a set of functions which spans the space of all torus amplitudes. Despite such characters being modular forms of inhomogeneous weight, they fit in the ADET-classification of fermionic sum representations. Thus, they show that logarithmic conformal field theories naturally have to be taken into account when attempting to classify rational conformal field theories.

Invited review article for a special issue of J. Phys. A on logarithmic conformal field theory, v2: references added, some clarifications, v3: references and some details added in section 3

References in corpus (14)

• Logarithmic extensions of minimal models: characters and modular transformations
• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
• Virasoro representations and fusion for general augmented minimal models
• Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
• Logarithmic torus amplitudes
• A modular invariant bulk theory for the c=0 triplet model
• Notes on instantons in topological field theory and beyond
• On Verlinde-Like Formulas in c_{p,1} Logarithmic Conformal Field Theories
• Three-Dimensional Tricritical Gravity
• W-Extended Fusion Algebra of Critical Percolation
• Fermionic Expressions for the Characters of c(p,1) Logarithmic Conformal Field Theories
• The structure of Zhu's algebras for certain W-algebras
• Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theory
• Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k

Cited by in corpus (3)

• Logarithmic conformal invariance in the Abelian sandpile model
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• Combinatorial Solution of the Eclectic Spin Chain