In
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
, a logarithmic conformal field theory is a
conformal field theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes ...
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.
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
In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as ...
.
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.
* The
Wess–Zumino–Witten model
In theoretical physics and mathematics, a Wess–Zumino–Witten (WZW) model, also called a Wess–Zumino–Novikov–Witten model, is a type of two-dimensional conformal field theory named after Julius Wess, Bruno Zumino, Sergei Novikov and Edwa ...
, based on the simplest non-trivial
supergroup Supergroup or super group may refer to:
* Supergroup (music), a music group formed by artists who are already notable or respected in their fields
* Supergroup (physics), a generalization of groups, used in the study of supersymmetry
* Supergroup ...
.
* The triplet model at
is also rational with respect to the triplet algebra.
References
Conformal field theory
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