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

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Authors

  • Michael Flohr
  • Michael Koehn

Research Organisations

External Research Organisations

  • Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
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Details

Original languageEnglish
Article number494007
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number49
Early online date20 Nov 2013
Publication statusPublished - 13 Dec 2013

Abstract

In this article, we review some aspects of logarithmic conformal field theories (LCFTs) 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 LCFTs 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 LCFTs naturally have to be taken into account when attempting to classify rational conformal field theories.

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Cite this

What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT. / Flohr, Michael; Koehn, Michael.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 49, 494007, 13.12.2013.

Research output: Contribution to journal › Article › Research › peer review

Flohr M, Koehn M. What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT. Journal of Physics A: Mathematical and Theoretical. 2013 Dec 13;46(49):494007. Epub 2013 Nov 20. doi: 10.48550/arXiv.1307.5844, 10.1088/1751-8113/46/49/494007
Flohr, Michael ; Koehn, Michael. / What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT. In: Journal of Physics A: Mathematical and Theoretical. 2013 ; Vol. 46, No. 49.
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