  We study the conformal bootstrap in fractional space-time dimensions,
obtaining rigorous bounds on operator dimensions. Our results show strong
evidence that there is a family of unitary CFTs connecting the 2D Ising model,
the 3D Ising model, and the free scalar theory in 4D. We give numerical
predictions for the leading operator dimensions and central charge in this
family at different values of D and compare these to calculations of phi^4
theory in the epsilon-expansion.
