  The $d=2$ critical Ising model is described by an exactly solvable Conformal
Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple
system at strong coupling outside of even dimensions. Using novel numerical and
analytical conformal bootstrap methods in Lorentzian signature, we show that
the leading corrections to the Ising data are more singular than $\epsilon$.
There must be infinitely many new states due to the $d$-dependence of conformal
symmetry. The linear independence of conformal blocks is central to this
bootstrap approach, which can be extended to more rigorous studies of
non-positive systems, such as non-unitary, defect/boundary and thermal CFTs.
