Modular Invariance

  • Malte Henkel
Part of the Texts and Monographs in Physics book series (TMP)


The result (10.46) for the operator content of the 2D Ising model raises a question: in principle, having three irreducible representations of the Virasoro algebra for m = 3, one could combine in 9 possible ways the holomorphic and antiholomorphic parts to obtain the primary operators. However, just the 5 found can be realized. A part of the explanation comes from the locality requirement for the correlation functions discussed in Chaps. 5–7. A finer explanation for this selection comes from the requirement of modular invariance for the partition function. The presentation follows the work of Cardy [137, 138, G14].


Partition Function Central Charge Vertex Operator Discrete Symmetry Modular Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Malte Henkel
    • 1
  1. 1.Laboratoire de Physique des Matériaux CNRS-UMR 7556Université Henri Poincaré Nancy IVandœuvre lès NancyFrance

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