Runkel-Watts theory is a 2d CFT with central charge $c = 1$. It can be constructed from the $A$-series of minimal models, which are parametrized by integers $p$ and which have central charge
$$ c = 1 - 6 \frac{1}{p(p+1)} \, . $$
The Runkel-Watts theory is defined as the limiting theory that arises from taking $p \to \infty$.
Generalizations to the theory defined above exist for certain rational values of $c < 1$. These may be constructed from Liouville theory by loosening the assumption that the correlation functions are meromorphic functions of the coupling constant and the conformal momentum. As a result, these theories have identical spectra to the Liouville with the same central charge, but their correlation functions differ.
These theories were originally discussed in this paper.
The generalization to $c < 1$ is discussed here