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Logarithmic conformal field theory

In the complex and diverse world in which we live, Logarithmic conformal field theory represents a topic of great relevance and interest to a wide audience. This article aims to explore the different aspects and perspectives of Logarithmic conformal field theory, from its historical origins to its impact today. Throughout these pages, we will delve into the multiple facets that make up Logarithmic conformal field theory, analyzing its social, political, economic and cultural implications. Through a multidisciplinary approach, this article seeks to offer a comprehensive and enriching vision of Logarithmic conformal field theory, inviting readers to reflect and question their own preconceptions about this fascinating topic.

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In theoretical physics, a logarithmic conformal field theory (LCFT) is a conformal field theory in which the correlators of the basic fields are allowed to be logarithmic at short distance, instead of being powers of the fields' distance. Equivalently, the dilation operator is not diagonalizable.[1]

Examples of logarithmic conformal field theories include critical percolation.

In two dimensions

Just like conformal field theory in general, logarithmic conformal field theory has been particularly well-studied in two dimensions.[2][3] Some two-dimensional logarithmic CFTs have been solved:

  • The Gaberdiel–Kausch CFT at central charge , which is rational with respect to its extended symmetry algebra, namely the triplet algebra.[4]
  • The Wess–Zumino–Witten model, based on the simplest non-trivial supergroup.[5]
  • The triplet model at is also rational with respect to the triplet algebra.[6]

References

  1. ^ Hogervorst, Matthijs; Paulos, Miguel; Vichi, Alessandro (2016-05-12). "The ABC (in any D) of Logarithmic CFT". Journal of High Energy Physics. 2017 (10) 201. arXiv:1605.03959v1. doi:10.1007/JHEP10(2017)201. S2CID 62821354.
  2. ^ Gurarie, V. (1993-03-29). "Logarithmic Operators in Conformal Field Theory". Nuclear Physics B. 410 (3): 535–549. arXiv:hep-th/9303160. Bibcode:1993NuPhB.410..535G. doi:10.1016/0550-3213(93)90528-W. S2CID 17344227.
  3. ^ Creutzig, Thomas; Ridout, David (2013-03-04). "Logarithmic Conformal Field Theory: Beyond an Introduction". Journal of Physics A: Mathematical and Theoretical. 46 (49) 494006. arXiv:1303.0847v3. Bibcode:2013JPhA...46W4006C. doi:10.1088/1751-8113/46/49/494006. S2CID 118554516.
  4. ^ Gaberdiel, Matthias R.; Kausch, Horst G. (1999). "A Local Logarithmic Conformal Field Theory". Nuclear Physics B. 538 (3): 631–658. arXiv:hep-th/9807091. Bibcode:1999NuPhB.538..631G. doi:10.1016/S0550-3213(98)00701-9. S2CID 15554654.
  5. ^ Schomerus, Volker; Saleur, Hubert (2006). "The GL(1 - 1) WZW model: From Supergeometry to Logarithmic CFT". Nucl. Phys. B. 734 (3): 221–245. arXiv:hep-th/0510032. Bibcode:2006NuPhB.734..221S. doi:10.1016/j.nuclphysb.2005.11.013. S2CID 16530989.
  6. ^ Runkel, Ingo; Gaberdiel, Matthias R.; Wood, Simon (2012-01-30). "Logarithmic Bulk and Boundary Conformal Field Theory and the Full Centre Construction". Conformal Field Theories and Tensor Categories. Mathematical Lectures from Peking University. pp. 93–168. arXiv:1201.6273v1. doi:10.1007/978-3-642-39383-9_4. ISBN 978-3-642-39382-2.


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