Abstract :
We construct in this paper a new class of conformal field theories (CFTʹs) in which the fields are characterized by equations of the biharmonic type. All these theories are interacting and admit an explicit Lagrangian formulation. For that reason, the biharmonic CFTʹs are useful in the study of interacting CFTʹs and can have also applications in string theories. Besides, it is possible to interprete the biharmonic CFTʹs as theories of conformal gravity in two dimensions, which represent an alternative to Liouville field theory.
