Abstract
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].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Henkel, M. (1999). Modular Invariance. In: Conformal Invariance and Critical Phenomena. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03937-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-03937-3_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08466-9
Online ISBN: 978-3-662-03937-3
eBook Packages: Springer Book Archive