Logarithmic conformal field theory

In theoretical physics, a logarithmic conformal field theory 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". arXiv.org. doi:10.1007/JHEP10(2017)201. Retrieved 2021-09-26.
  2. Gurarie, V. (1993-03-29). "Logarithmic Operators in Conformal Field Theory". arXiv.org. doi:10.1016/0550-3213(93)90528-W. Retrieved 2021-09-26.
  3. Creutzig, Thomas; Ridout, David (2013-03-04). "Logarithmic Conformal Field Theory: Beyond an Introduction". arXiv.org. doi:10.1088/1751-8113/46/49/494006. Retrieved 2021-09-26.
  4. Gaberdiel, Matthias R.; Kausch, Horst G. (1998-07-13). "A Local Logarithmic Conformal Field Theory". arXiv.org. doi:10.1016/S0550-3213(98)00701-9. Retrieved 2021-09-26.
  5. Schomerus, Volker; Saleur, Hubert (2005-10-04). "The GL(1 - 1) WZW model: From Supergeometry to Logarithmic CFT". arXiv.org. doi:10.1016/j.nuclphysb.2005.11.013. Retrieved 2021-09-26.
  6. Runkel, Ingo; Gaberdiel, Matthias R.; Wood, Simon (2012-01-30). "Logarithmic bulk and boundary conformal field theory and the full centre construction". arXiv.org. Retrieved 2021-09-26.


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