An important example of conformal field theory is the 2d Ising model, more precisely its scaling limit when the size of the lattice goes to zero. I am not an expert in the field, but this is the only description of this specific field theory I have seen in the literature.

**Question.** Can the above conformal field theory be described by a conformally invariant Lagrangian?

Any feedback, ideally a reference, will be helpful.