  Under the assumption that degenerate fields exist, diagonal CFTs such as
Liouville theory can be solved analytically using the conformal bootstrap
method. Here we generalize this approach to non-diagonal CFTs, i.e. CFTs whose
primary fields have nonzero conformal spins. Assuming generic values of the
central charge, we find that the non-diagonal sector of the spectrum must be
parametrized by two integer numbers. We then derive and solve the equations
that determine how three- and four-point structure constants depend on these
numbers. In order to test these results, we numerically check crossing symmetry
of a class of four-point functions in a non-rational limit of D-series minimal
models. The simplest four-point functions in this class were previously argued
to describe connectivities of clusters in the critical Potts model.
