Logarithmic conformal field theory

Conformal field theory with logarithmic short distance behavior

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

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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  c = − 2 {\displaystyle c=-2} , which is rational with respect to its extended symmetry algebra, namely the triplet algebra.[4]
* The  G L ( 1 | 1 ) {\displaystyle GL(1|1)} Wess–Zumino–Witten model, based on the simplest non-trivial supergroup.[5]
* The triplet model at  c = 0 {\displaystyle c=0} is also rational with respect to the triplet algebra.[6]

## References

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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].

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