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.
Just like conformal field theory in general, logarithmic conformal field theory has been particularly well-studied in two dimensions.
Examples of logarithmic conformal field theories include critical percolation.
References
In arbitrary dimensions
Hogervorst, Matthijs; Paulos, Miguel; Vichi, Alessandro (2017). "The ABC (in any D) of logarithmic CFT". Journal of High Energy Physics. 2017 (10). doi:10.1007/jhep10(2017)201. ISSN 1029-8479.
In two dimensions
T. Creutzig, D. Ridout, Logarithmic Conformal Field Theory: Beyond an Introduction.
V. Gurarie, Logarithmic operators in conformal field theory, Nuclear Physics B 410 (1993) 535-549.
M. R. Gaberdiel, H. G. Kausch, Indecomposable fusion products, Nuclear Physics B 477 (1996) 293-318.
M. Reza Rahimi Tabar, A. Aghamohammadi and M. Khorrami, The logarithmic conformal field theories, Nuclear Physics B 497 (1997) 555-566.
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