  Recently an efficient numerical method has been developed to implement the
constraints of crossing symmetry and unitarity on the operator dimensions and
OPE coefficients of conformal field theories (CFT) in diverse space-time
dimensions. It appears that the calculations can be done only for theories
lying at the boundary of the allowed parameter space. Here it is pointed out
that a similar method can be applied to a larger class of CFT's, whether
unitary or not, and no free parameter remains, provided we know the fusion
algebra of the low lying primary operators. As an example we calculate using
first principles, with no phenomenological input, the lowest scaling dimensions
of the local operators associated with the Yang-Lee edge singularity in three
and four space dimensions. The edge exponents compare favorably with the latest
numerical estimates. A consistency check of this approach on the 3d critical
Ising model is also made.
