  We explore the space of extremal functionals in the conformal bootstrap. By
recasting the bootstrap problem as a set of non-linear equations parameterized
by the CFT data, we find an efficient algorithm for converging to the extremal
solution corresponding to the boundary of allowed regions in the parameter
space of CFTs. Furthermore, by deforming these solutions, we demonstrate that
certain solutions corresponding to known theories are continuously connected.
Employing these methods, we will explore the space of non-unitary CFTs in the
context of modular as well as correlation function bootstrap. In two
dimensions, we show that the extremal solution corresponding to the Ising model
is connected to that of the Yang-Lee minimal model. By deforming this solution
to three dimensions, we provide evidence that the CFT data obtained in this way
is compatible with the $\epsilon$-expansion for a non-unitary theory.
