Logarithmic conformal field theory

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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:

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). 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". arXiv: 1201.6273v1 [hep-th].