Unitary conformal field theories (CFTs) with irrational (or including the special case of rational) central charge is called irrational conformal field theory (ICFT).
Irrational conformal field theory (ICFT) is said to include all conformal field theories, and, in particular, ICFT includes rational conformal field theory (RCFT).
ICFT $\supset$ RCFT.
RCFT is only a tiny subset inside ICFT.
However, do we have examples of non-unitary Conformal Field Theory (NUCFT)? If so, what are the relations between:
- unitary RCFT
- unitary ICFT
- non-unitary RCFT
- non-unitary ICFT
Are there good quantum mechanical lattice realizations of these CFTs?
What are the relations of their sets?