In theoretical physics, a logarithmic conformal field theory is a conformal field theory in which thecorrelators 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.
Examples of logarithmic conformal field theories include critical percolation.
Just like conformal field theory in general, logarithmic conformal field theory has been particularly well-studied in two dimensions. Some two-dimensional logarithmic CFTs have been solved:
c=-2
GL(1|1)
c=0